# data[].attributes.body
Ask fellow testtakers in the AP Physics Reddit Community.

# data[].attributes.attachment_link.description
Practice questions in the fundamentals of physics while you review topics from classical dynamics to modern quantum mechanics with Albert's AP® Physics 1 exam prep.

# data[].attributes.body
Post your questions in the APStudents Reddit Forum.

# data[].attributes.body
We value your opinion and would love to hear your feedback! Your input helps us create more learning paths. Please like the cards with helpful resources, leave comments, or email us at apphysics.learningpath@gmail.com. Thank you!

# data[].attributes.attachment_link.description
Learning Goal: Concept 1: Translational Equilibrium Concept 2: Torque at 90 Degrees Concept 3: Torque NOT at 90 Degrees Concept 4: Rotational Kinematics Concept 5: Torque…

# data[].attributes.attachment_link.title
Torque, Basic Introduction, Lever Arm, Moment of Force, Simple Machines & Mechanical Advantage

# data[].attributes.attachment_link.title
Rotational Kinematics Physics Problems, Basic Introduction, Equations & Formulas

# data[].attributes.attachment_link.title
Rotational Motion Physics, Basic Introduction, Angular Velocity & Tangential Acceleration

# data[].attributes.body
12%–18%

# data[].attributes.attachment_link.title
Simple Harmonic Motion Introduction(SHM) via a Horizontal Mass-Spring System (AP Physics 1/JEE/NEET)

# data[].attributes.attachment_link.title
Energy In a Simple Harmonic Oscillator - Maximum Velocity & Acceleration Calculations

# data[].attributes.attachment_link.title
Simple Harmonic Motion, Mass Spring System - Amplitude, Frequency, Velocity - Physics Problems

# data[].attributes.body
4%-6% of exam score

# data[].attributes.attachment_link.title
AP Physics 1 – Momentum – Mr. Lam’s Classroom

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# data[].attributes.attachment_link.title
Linear momentum and collisions | AP®︎ Physics 1 | Science | Khan Academy

# data[].attributes.attachment_link.description
Momentum ties velocity and mass into one quantity. It might not be obvious why this is useful, but momentum has this cool property where the total amount of it never changes. This is called the conservation of momentum, and we can use it to analyze collisions and other interactions. Bam!

# data[].attributes.attachment_link.title
Introduction to Momentum, Force, Newton's Second Law, Conservation of Linear Momentum, Physics

# data[].attributes.headline
Long Length Article (With Questions): Conservation of Linear Momentum

# data[].attributes.subject
Long Length Article (With Questions): Conservation of Linear Momentum

# data[].attributes.attachment_link.description
Two colliding object experience equal-strength forces that endure for equal-length times and result ini equal amounts of impulse and momentum change. As such, the momentum change of one object is equal (and oppositely-directed) tp the momentum change of the second object. If one object gains momentum, the second object loses momentum and the overall amount of momentum possessed by the two objects is the same before the collision as after the collision. We say that momentum is conserved.

# data[].attributes.headline
Short Video: Conservation of Linear Momentum

# data[].attributes.subject
Short Video: Conservation of Linear Momentum

# data[].attributes.body
Click on image to read full text

# data[].attributes.attachment_link.readable_text
Color Coding: 

White - Miscellaneous
Red - Articles/ Relevant Websites
Yellow - Videos
Green - Topic Value in Exam
Blue - Flashcards
Purple - Worksheets


Important Information: 
The Padlet follows a pattern. As you scroll to the right, you will see that we subdivided AP Physics into their 7 individual units, 
as seen on the following website: https://apstudents.collegeboard.org/courses/ap-physics-1-algebra-based. If you scroll under 
those categories, you will see that it is typically structured as follows: There are a few videos or a playlist at the beginning that 
serve as a review of the entire unit, if you do not need to study that unit that much. After you continue to scroll there are new 
sections, typically divided by new videos with the title of the subtopic. Afterwards there is usually an article and then a worksheet. 
At the bottom of each unit we have included flashcards found online (typically on quizlet). The subtopics can be found on the 
same website linked before. The videos and articles are also labeled by length: Short, medium, and long left to our padlet editors' 
discretion as to what qualifies as a short/mid/long video or article, so you may have to take those descriptions with a grain of salt. 

We hope you are able to get good use out of the padlet!

# data[].attributes.headline
Library of AP Physics 1 Practice and Study Material

# data[].attributes.subject
Library of AP Physics 1 Practice and Study Material

# data[].attributes.attachment_link.title
Identifying Open & Closed Momentum Systems | Physics | Study.com

# data[].attributes.attachment_link.description
Learn how to identify open and closed momentum systems, and see examples that walk through sample problems step-by-step for you to improve your physics knowledge and skills.

# data[].attributes.attachment_link.title
Momentum - Open and Closed Systems - IB Physics

# data[].attributes.headline
Mid Length Video: Open and Closed Systems

# data[].attributes.subject
Mid Length Video: Open and Closed Systems

# data[].attributes.body
Medium length video with a short explanation and some problems that are worked through. Also includes a description of relation to mechanical energy.

# data[].attributes.attachment_link.title
Open vs Closed Systems and Total Mechanical Energy & Momentum (AP Physics 1)

# data[].attributes.attachment_link.title
Changes in Momentum Worked Examples | Momentum and Impulse | AP Physics 1 | Khan Academy

# data[].attributes.body
momentum_and_impulse.pdf (sfponline.org)

# data[].attributes.attachment_link.title
Impulse and Momentum - Formulas and Equations - College Physics

# data[].attributes.attachment_link.title
What are momentum and impulse? (article) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.body
A lot of examples and practice problems.

# data[].attributes.attachment_link.title
AP Physics 1 - Unit 5: Momentum - YouTube

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.headline
Video Playlist: (incomplete) Unit Overview

# data[].attributes.subject
Video Playlist: (incomplete) Unit Overview

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.body
12%-18% of exam score

# data[].attributes.attachment_link.readable_text
In a previous part of Lesson 1, it was said that work is done upon an object whenever a force acts upon it to cause it to be displaced. Work involves a force acting upon an object to cause a displacement. In all instances in which work is done, there is an object that supplies the force in order to do the work. If a World Civilization book is lifted to the top shelf of a student locker, then the student supplies the force to do the work on the book. If a plow is displaced across a field, then some form of farm equipment (usually a tractor or a horse) supplies the force to do the work on the plow. If a pitcher winds up and accelerates a baseball towards home plate, then the pitcher supplies the force to do the work on the baseball. If a roller coaster car is displaced from ground level to the top of the first drop of a roller coaster ride, then a chain driven by a motor supplies the force to do the work on the car. If a barbell is displaced from ground level to a height above a weightlifter's head, then the weightlifter is supplying a force to do work on the barbell. In all instances, an object that possesses some form of energy supplies the force to do the work. In the instances described here, the objects doing the work (a student, a tractor, a pitcher, a motor/chain) possess chemical potential energy stored in food or fuel that is transformed into work. In the process of doing work, the object that is doing the work exchanges energy with the object upon which the work is done. When the work is done upon the object, that object gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy.
Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position). A moving car possesses mechanical energy due to its motion ( kinetic energy). A moving baseball possesses mechanical energy due to both its high speed ( kinetic energy) and its vertical position above the ground (gravitational potential energy). A World Civilization book at rest on the top shelf of a locker possesses mechanical energy due to its vertical position above the ground (gravitational potential energy). A barbell lifted high above a weightlifter's head possesses mechanical energy due to its vertical position above the ground (gravitational potential energy). A drawn bow possesses mechanical energy due to its stretched position (elastic potential energy).

Mechanical Energy as the Ability to Do Work

An object that possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Any object that possesses mechanical energy - whether it is in the form of potential energy or kinetic energy - is able to do work. That is, its mechanical energy enables that object to apply a force to another object in order to cause it to be displaced.

Numerous examples can be given of how an object with mechanical energy can harness that energy in order to apply a force to cause another object to be displaced. A classic example involves the massive wrecking ball of a demolition machine. The wrecking ball is a massive object that is swung backwards to a high position and allowed to swing forward into building structure or other object in order to demolish it. Upon hitting the structure, the wrecking ball applies a force to it in order to cause the wall of the structure to be displaced. The diagram below depicts the process by which the mechanical energy of a wrecking ball can be used to do work.

A hammer is a tool that utilizes mechanical energy to do work. The mechanical energy of a hammer gives the hammer its ability to apply a force to a nail in order to cause it to be displaced. Because the hammer has mechanical energy (in the form of kinetic energy), it is able to do work on the nail. Mechanical energy is the ability to do work.

Another example that illustrates how mechanical energy is the ability of an object to do work can be seen any evening at your local bowling alley. The mechanical energy of a bowling ball gives the ball the ability to apply a force to a bowling pin in order to cause it to be displaced. Because the massive ball has mechanical energy (in the form of kinetic energy), it is able to do work on the pin. Mechanical energy is the ability to do work.

A dart gun is still another example of how mechanical energy of an object can do work on another object. When a dart gun is loaded and the springs are compressed, it possesses mechanical energy. The mechanical energy of the compressed springs gives the springs the ability to apply a force to the dart in order to cause it to be displaced. Because of the springs have mechanical energy (in the form of elastic potential energy), it is able to do work on the dart. Mechanical energy is the ability to do work.

A common scene in some parts of the countryside is a "wind farm." High-speed winds are used to do work on the blades of a turbine at the so-called wind farm. The mechanical energy of the moving air gives the air particles the ability to apply a force and cause a displacement of the blades. As the blades spin, their energy is subsequently converted into electrical energy (a non-mechanical form of energy) and supplied to homes and industries in order to run electrical appliances. Because the moving wind has mechanical energy (in the form of kinetic energy), it is able to do work on the blades. Once more, mechanical energy is the ability to do work.

The Total Mechanical Energy

As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).

TME = PE + KE

As discussed earlier, there are two forms of potential energy discussed in our course - gravitational potential energy and elastic potential energy. Given this fact, the above equation can be rewritten:

TME = PEgrav + PEspring + KE

The diagram below depicts the motion of Lee Ben Fardest (esteemed American ski jumper) as he glides down the hill and makes one of his record-setting jumps.

The total mechanical energy of Lee Ben Fardest is the sum of the potential and kinetic energies. The two forms of energy sum up to 50 000 Joules. Notice also that the total mechanical energy of Lee Ben Fardest is a constant value throughout his motion. There are conditions under which the total mechanical energy will be a constant value and conditions under which it will be a changing value. This is the subject of Lesson 2 - the work-energy relationship. For now, merely remember that total mechanical energy is the energy possessed by an object due to either its motion or its stored energy of position. The total amount of mechanical energy is merely the sum of these two forms of energy. And finally, an object with mechanical energy is able to do work on another object.

# data[].attributes.attachment_link.description
In a previous part of Lesson 1, it was said that work is done upon an object whenever a force acts upon it to cause it to be displaced. Work involves a force acting upon an object to cause a displacement.

# data[].attributes.headline
Mid Length Article: Open and Closed Systems of Energy

# data[].attributes.subject
Mid Length Article: Open and Closed Systems of Energy

# data[].attributes.attachment_link.readable_text
Figure 1 (https://www.khanacademy.org/science/physics/ap-physics-1/ap-work-and-energy/modal/a/work-ap-physics-1)

GRAPH
The force applied to an object can be graphed as a function of the position of the object. Area under a F V.S. Δ x graph is the energy transferred through working. Areas above the position axis are positive work and areas below the axis are negative work. If the force is not constant, we can divide the graph into sections with simpler shapes and add up the work in each section.

For example, to find the total work done on the object described in Figure 1, we can say: ​

# data[].attributes.attachment_link.description
KEY TERMS Energy (E) - Measurement of the ability to do work. But really, energy is the thing that allows us to make changes. SI unit is joule (J). Work (W) - A transfer of energy. But better, work...

# data[].attributes.headline
 Short Article: Conservation of Energy Review

# data[].attributes.subject
 Short Article: Conservation of Energy Review

# data[].attributes.attachment_link.title
Conservation of energy review (article) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.headline
Worksheet - Kinetic and Potential Energy

# data[].attributes.subject
Worksheet - Kinetic and Potential Energy

# data[].attributes.body
AP Physics1 KE and PE Worksheet | PDF | Kinetic Energy | Potential Energy (scribd.com)

# data[].attributes.headline
Worksheet - Work, Energy, Conservation of Energy

# data[].attributes.subject
Worksheet - Work, Energy, Conservation of Energy

# data[].attributes.body
https://www.crashwhite.com/apphysics/materials/practicetests/practice_test-4-work-energy.pdf

# data[].attributes.body
AP Physics Unit 4: Energy | 368 plays | Quizizz

# data[].attributes.headline
Video Playlist: Alternative Overview (with practice problems)

# data[].attributes.subject
Video Playlist: Alternative Overview (with practice problems)

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.body
20%-28% of exam score

# data[].attributes.headline
Long Video: Free-body diagrams for objects in uniform circular motion

# data[].attributes.subject
Long Video: Free-body diagrams for objects in uniform circular motion

# data[].attributes.attachment_link.title
Uniform Circular Motion Free Body Diagrams

# data[].attributes.headline
Short Video: Centripetal acceleration vs. centripetal force

# data[].attributes.subject
Short Video: Centripetal acceleration vs. centripetal force

# data[].attributes.attachment_link.title
Uniform Circular Motion and Centripetal Force

# data[].attributes.headline
Midlength Article: Centripetal acceleration vs. centripetal force

# data[].attributes.subject
Midlength Article: Centripetal acceleration vs. centripetal force

# data[].attributes.attachment_link.readable_text
Equation:

Force and acceleration are both quantities that have both magnitude and direction. The direction of the net force acting on an object is the same as the direction of its acceleration. This means that if you want to change the direction of an object's acceleration, you need to change the direction of the net force acting on it. For example, if you want to change the direction of a car's acceleration so it is accelerating and turning right, you need to give it a rightward net force.

The center of mass (COM) of a system is a point that represents the average position of all the mass in the system. Conceptually, it is the point where the entire mass of the system can be considered to be concentrated, which makes it the point at which the system would balance if it were suspended by a single point. The position of the center of mass depends on the distribution of mass within the system.

Consider a seesaw in a playground. The center of mass of a seesaw is located at the point where the board of the seesaw balances. This point is also known as the pivot point. If you place a heavier person on one side of the seesaw, the center of mass will shift closer to that side, and the seesaw will tilt in that direction.

For example, if you want to know how fast a car is moving, you can measure its velocity. If you want to know how fast the car's velocity is changing, you can measure its acceleration. Similarly, if you want to know how fast the center of mass of a system is moving, you can measure its center of mass velocity, and if you want to know how fast the center of mass velocity is changing, you can measure the acceleration of the center of mass.

While the centripetal acceleration points towards the center of the circle, the velocity vector does not. A key element of uniform circular motion is that the velocity is kept constant, so in order to have acceleration due to a change in direction only, the velocity vector must be tangent to the acceleration vector at all points along the circle. Tangent means that the velocity vector makes a 90-degree angle with the centripetal acceleration vector when the vectors are placed tail to tail.

Since the velocity and acceleration vectors make a 90-degree angle, there is no component of the centripetal acceleration that is acting in the same direction as the velocity vector, so the acceleration will not affect the magnitude of the velocity. However, the acceleration vector does affect the direction of the velocity vector. If you add the acceleration and velocity vectors using vector addition, you will find that the direction of the resultant vector is always pointing along the circle, causing uniform circular motion.

We can relate the centripetal acceleration to the tangential velocity using this equation:

where a is the centripetal acceleration, v is the velocity, and r is the radius of the circle.

It's also important to note that the greater the speed of an object, the greater the centripetal force required to keep it moving in a circular path. Similarly, the smaller the radius of a circular path, the greater the centripetal force required to keep an object moving in that path.

1. What is the direction of the centripetal acceleration of an object undergoing uniform circular motion? A) Radial B) Tangential C) Perpendicular D) Horizontal

Answer: A) Radial

2. An object of mass 5 kg is moving in a circular path of radius 3 m with a constant velocity of 4 m/s. What is the centripetal acceleration of the object? A) 12 m/s^2 B) 16 m/s^2 C) 20 m/s^2 D) 5.33 m/s^2

3. A ball of mass 1 kg is tied to a string and is moving in a circular path of radius 0.5 m. If the ball is moving with a velocity of 3 m/s, what is the centripetal force acting on the ball? A) 2.25 N B) 4.5 N C) 9 N D) 1.5 N

Answer: D) 1.5 N Explanation: The centripetal force acting on an object in uniform circular motion is given by the formula F = m * a_c, where F is the centripetal force, m is the mass of the object and a_c is the centripetal acceleration. To find the centripetal acceleration, we use the formula a_c = v^2/r, where a_c is the centripetal acceleration, v is the velocity of the object and r is the radius of the circular path. By substituting the given values, we get a_c = (3 m/s)^2 / 0.5 m = 9 m^2/s^2 / 0.5 m = 18 m/s^2Then we can use the formula F = m * a_c to find the centripetal force acting on the ball, we know the mass of the ball is 1 kg, so we substitute the values into the formula: F = m * a_c = 1 kg * 18 m/s^2 = 18 N

# data[].attributes.attachment_link.title
Centripetal Acceleration and Centripetal Force - AP Physics 1 Study Guide 2024 | Fiveable

# data[].attributes.attachment_link.description
Cram for AP Physics 1 - Circular Motion & Gravitation with Fiveable Study Guides. Includes key concepts, notes, vocab, and practice quizzes.

# data[].attributes.headline
Short Video: Inertial vs. gravitational mass

# data[].attributes.subject
Short Video: Inertial vs. gravitational mass

# data[].attributes.attachment_link.title
Inertial Mass vs. Gravitational Mass | Circular motion and gravitation | AP Physics 1 | Khan Academy

# data[].attributes.headline
Short Article: Inertial vs. gravitational mass

# data[].attributes.subject
Short Article: Inertial vs. gravitational mass

# data[].attributes.attachment_link.title
What is the difference between the inertial and gravitational mass?

# data[].attributes.attachment_link.description
Ask the experts your physics and astronomy questions, read answer archive, and more.

# data[].attributes.headline
Midlength Video: Gravitational field/acceleration due to gravity on different planets

# data[].attributes.subject
Midlength Video: Gravitational field/acceleration due to gravity on different planets

# data[].attributes.attachment_link.title
Gravity, Universal Gravitation Constant - Gravitational Force Between Earth, Moon & Sun, Physics

# data[].attributes.headline
Short Article: Gravitational field/acceleration due to gravity on different planets

# data[].attributes.subject
Short Article: Gravitational field/acceleration due to gravity on different planets

# data[].attributes.attachment_link.readable_text
A gravitational field g at the location of an object with mass m causes a gravitational force of magnitude mg to be exerted on the object in the direction of the field.

Based on this free-body diagram of a satellite orbiting a planet, we know that F, the force of the planet's gravity, is the only force acting in the direction of the net force of the satellite. Since the satellite is in circular motion, the velocity of the satellite is not included in the net force calculation since it is tangent to the circle. We can now use Newton's Second Law and Newton's Universal Law of Gravitation to relate the force between the satellite and the planet like this:

In this equation, m1 is the mass of the satellite and m2 is the mass of the planet. We use m1 on the right side of the expression because we are analyzing the forces acting on the satellite, not on the planet. From this equation, we can see that there is an m1 term on both sides of the equation so we can divide through by m1 to obtain:

Since the acceleration is caused only by the gravitational force, we know that this is the equation for the acceleration of gravity, g.

This equation can be used to determine the acceleration of gravity for any planet given its mass and radius. To recap, in this equation, g is the gravitational field in m/s/s, G is the universal gravitation constant 6.7 x 10^-11 N * m^2/kg^2, r is the radius in meters, and m is the mass in kilograms.

1. How does the gravitational acceleration (g) on the surface of a planet change if the mass of the planet is doubled? a) It remains the same b) It is halved c) It is doubled d) It is quadrupled Answer: c) It is doubled

2. A planet has a mass of 6 x 10^24 kg and a radius of 6 x 10^6 m. Calculate the gravitational acceleration (g) on its surface.

a) 7.2 m/s^2

b) 9.8 m/s^2

c) 10.4 m/s^2

d) 18.6 m/s^2 Answer: d) 9.8 m/s^2

Explanation: g = Gm/r^2 = (6.67 x 10^-11 N*(m^2)/(kg^2))(6 x 10^24 kg) / (6 x 10^6 m)^2 = 9.8 m/s^2

3. How does the strength of the gravitational field change if the distance between two masses is doubled? a) It remains the same b) It is halved c) It is quartered d) It is doubled Answer: c) It is quartered

4. An object is located at a distance of 2 x 10^8 m from a star with a mass of 2 x 10^30 kg. Calculate the gravitational force (F) acting on the object.

a) -3.35 x 10^-6 N b) -4.92 x 10^-12 N c) -5.98 x 10^-9 N d) -6.67 x 10^-11 N Answer: d) -6.67 x 10^-11 N

Explanation: F = Gm1m2/r^2 = (6.67 x 10^-11 N*(m^2)/(kg^2))(2 x 10^30 kg)(1 kg) / (2 x 10^8 m)^2 = 6.67 x 10^-11 N

🎥Watch: AP Physics 1 - Unit 3 Streams

# data[].attributes.attachment_link.title
Gravitational Field/Acceleration Due to Gravity on Different Planets - AP Physics 1 Study Guide 2024 | Fiveable

# data[].attributes.attachment_link.description
Cram for AP Physics 1 - Circular Motion & Gravitation with Fiveable Study Guides. Includes key concepts, notes, vocab, and practice quizzes.

# data[].attributes.headline
Short Video: Gravitation and Electric Forces

# data[].attributes.subject
Short Video: Gravitation and Electric Forces

# data[].attributes.headline
Long Article: Gravitational and Electric Forces

# data[].attributes.subject
Long Article: Gravitational and Electric Forces

# data[].attributes.attachment_link.description
Gravitational and Electric Forces: ✓ Meaning ✓ Comparison ✓ Examples ✓ Differences ✓ StudySmarter Original

# data[].attributes.attachment_link.title
The Four Fundamental Forces of nature - Origin & Function

# data[].attributes.attachment_link.readable_text
Gravitational forces are exerted at all scales and dominate at the largest distances and mass scales.

The Force of Gravity or Weight is given as mass times acceleration due to gravity (mg). From this equation, we can gain the knowledge that the larger an object's mass, the more magnitude the force of gravity will garner.

Moreover, on astronomical scales gravity dominates over the other fundamental forces: the strong force, electromagnetic force, and the electroweak force. Despite the fact that gravity is usually the weakest of the four fundamental forces there are two key factors that help it dominate on this specific scale: gravity has an infinite range, and there is no negative mass.

The Strong Force - binds the fundamental particles of matter together to form larger particles

Electromagnetic Force - acts between charged particles

The Electroweak Force - particle decay

Gravity - the attraction between two objects that have mass or energy

For the purposes of AP Physics 1, you only need to understand the strong force and gravity. The strong force is the force that holds the nucleus of an atom together and is responsible for the stability of atomic nuclei. The strong force has a very short range and only acts between particles that are very close to each other. As the particles get farther apart, the magnitude of the strong force decreases.

At the largest distances, the gravitational force dominates over other forces, such as the strong force. This is because the gravitational force is extremely long-range, meaning that it can act over large distances. For example, the gravitational force between the Earth and the Sun is what keeps the Earth in its orbit around the Sun. Even though the Sun is 93 million miles away from the Earth, the gravitational force between them is strong enough to keep the Earth in its orbit. Recall that the strong force decreases as distance increases, so it would not have a large magnitude in this situation.

At the largest mass scales, gravity is dominant because it is the only force that can act over such massive bodies. For example, gravity is the force that holds galaxies together. The gravitational force between the stars and planets in a galaxy is strong enough to keep them all in orbit around the galaxy's center of mass.

Gravity is a long-range force because the strength of the gravitational force between two objects decreases only as the square of the distance between them (this idea is explored more in the next guide). This means that as the distance between two objects increases, the strength of the gravitational force between them decreases, but it does not decrease as quickly as it would for a short-range force.

For example, if you double the distance between two objects, the strength of the gravitational force between them will decrease to one-fourth of its original value. If you triple the distance, the strength of the gravitational force will decrease to one-ninth of its original value.

On the other hand, for a short-range force such as the strong nuclear force, the strength of the force decreases exponentially with the distance. That means that as the distance between two objects increases, the strength of the force decreases much more quickly than it would with gravity.

🎥Watch: AP Physics 1 - Unit 3 Streams

# data[].attributes.attachment_link.title
Fundamental Forces - AP Physics 1 Study Guide 2024 | Fiveable

# data[].attributes.attachment_link.description
Cram for AP Physics 1 - Circular Motion & Gravitation with Fiveable Study Guides. Includes key concepts, notes, vocab, and practice quizzes.

# data[].attributes.attachment_link.readable_text
Vector fields represent fluid flow (among many other things). They also offer a way to visualize functions whose input space and output space have the same dimension.

What we're building to

A vector field associates a vector with each point in space.

Vector field and fluid flow go hand-in-hand together.

You can think of a vector field as representing a multivariable function whose input and output spaces each have the same dimension.

The length of arrows drawn in a vector field are usually not to scale, but the ratio of the length of one vector to another should be accurate. Sometimes vector length is communicated using color.

Warmup: Drawing motion using velocity vectors

How do you draw a moving object? One way, common in math and physics, is to attach the velocity vector describing that object's movement to the drawing.

The length (magnitude) of the vector indicates the speed.

The direction of the vector indicates which way the object is moving.

There are two important conventions to notice in this example:

The description of a vector only tells us its magnitude and direction (e.g. meters per second to the left), but not where to draw the vector. The choice to attach the tail of the vector to the object whose movement it represents is just a convention.

The actual lengths of the vectors in our drawing don't really matter, just as long as the vector attached to the fox is twice as long as the one attached to the whale. You can just tell the person looking at the image "whatever the length of the arrow I just drew off the fox, that's what meters per second should look like."

Motivating example: Flowing fluids in two dimensions

Now let's kick it up a notch. What instead of depicting the motion of one or two objects, you had a fluid that was flowing in some particular manner. For example, the following animation depicts such a fluid flow by showing the motion of just a few fluid particles (drawn as blue dots):

To represent this kind of motion, we need to convey much more information than just a magnitude and a direction. We need to express the velocity of every individual particle in the fluid.

Actually, when it comes to drawing this motion, we can get away with representing only a sample of the particles. For instance, if you draw a velocity vector on each of the particles shown in the animation, and if you add some coordinate axes to keep track of where everything is, you might get a diagram that looks like this:

If you let your eyes follow the arrows in the image, moving from one to the next, you can get a very good feel for how the fluid it represents flows, even though it is a static image. Particles near each other tend to move at the same speed and direction. Therefore, each arrow not only represents the velocity of the individual particle it is attached to, but it also gives a feel for how the neighborhood of particles around it moves.

A diagram like this is called a vector field.

One important thing to mention about the way people typically draw vector fields is that vectors are almost never drawn to scale. For example, if an individual fluid particle was moving at meters per second, we should technically make the arrow attached to it units long, but that could span the entire image! If there were really long arrows attached to each point, directed every which way, the diagram could be a real mess.

As a result, it's common to scale each vector down so that they all fit cleanly in the image. What's important is not the specific length of any one vector, but how the lengths of different vectors compare to each other.

Another way some graphing software represents relative length is to color each vector. For instance, the following image shows the same vector field using colors: Dark blue arrows should be understood to be "shorter" than light blue arrows, even though technically they are all the same length.

Let's think about what a vector field is mathematically. Each point in two-dimensional space is associated with a two-dimensional vector. We can think of this as a (multivariable) vector-valued function, whose input is a point in two-dimensional space, and whose output is a two-dimensional vector.

For example, the function I used to generate the fluid flow and vector field above is

Since both the input and the output of this function have two coordinates, trying to graph it would require four dimensions. But with only a two-dimensional drawing we've represented it almost completely! What's more, this image gives a much better intuition for the swirling fluid it is meant to represent than a graph ever could.

Example 1: The identity function

When you do this at many more points in the plane, and scale all the vectors so that they don't get too messy, you get an image like this:

Example 3: Using graphs for help

Practice makes perfect, so let's look at one more vector-valued function in two dimensions and reason about what the vector field it represents should look like. Thinking this through is a little bit more involved than the previous examples.

Since does not appear anywhere in the output, the vectors in our field will remain unchanged as we pan left and right (why?).

Now take a look again at our vector field's function.

The -component of each vector will be slightly negative (i.e. they will point down) when is between and . As gets farther away from that range, going either up or down on the plane, the -component of the vector will be increasingly positive, so each vector will point more and more up. Sketching this out, you might get something like this:

Vector fields in three dimensions

We could do the same thing in three dimensions, perhaps modeling air currents. Analogous to the two-dimensional case, we associate each point in three-dimensional space with a three-dimensional vector and draw only a sample of those vectors.

The following video shows what such a three-dimensional vector field might look like, with colors closer to red indicating longer vectors and colors closer to blue indicating shorter vectors.

Drawing three-dimensional vector fields can be difficult, and even when we do, perhaps with some graphics software, the vectors can get in each other's way so that it's hard to see what's happening. As a result, this is one of those visualizations that is very useful as a loose idea to hold in your head, but not necessarily useful for precise representations.

A vector field associates a vector with each point in space.

Vector field and fluid flow go hand-in-hand together.

You can think of a vector field as representing a multivariable function whose input and output spaces each have the same dimension.

The length of arrows drawn in a vector field are usually not to scale, but the ratio of the length of one vector to another should be accurate. Sometimes vector length is communicated using color.

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.attachment_link.description
Study guides & practice questions for 8 key topics in AP Physics 1 Unit 3 - Circular Motion & Gravitation

# data[].attributes.body
6% - 8% of exam score

# data[].attributes.headline
Long Article: Applications of Newton's Second Law

# data[].attributes.subject
Long Article: Applications of Newton's Second Law

# data[].attributes.attachment_link.readable_text
Last Updated on April 11, 2023 by Sara Assem

Newton's laws of motion are three physical laws that establish the science of kinematics. These laws describe the relationship between the motion of an object and the force acting on it. They are essential because they are the foundation of classical mechanics, one of the main branches of physics. It was who established these laws, and he used these laws to explain many physical systems and phenomena.

In this article, we will focus on the most common examples and applications of Newton's second law of motion in daily life.

Newton's second law studies the movement of an object when external forces affect it. When a constant force affects a huge object, it causes it to accelerate, that is, to change its speed, at a constant rate.

Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.

discover praxilabs the best lab simulation

If we are going to talk about classical mechanics and applications of Newton's second law of motion in daily life, we must first shed light on the founder of these laws and the one who has the credit for bringing them out to us, Sir Isaac Newton. Here are some quick facts about Isaac Newton.

Newton's laws of motion were first published by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica in 1687 in 1687, which is the basis of . Newton used these laws to explain and investigate many physical phenomena. Newton showed that these laws in addition to the law of universal gravitation are able to explain , and these laws are still among the most important physical laws so far. Kepler's laws of planetary motion

For more information about Sir Isaac Newton and the other laws of motions, visit our article Applications of Newton's Laws of Motion in Daily Life.

"If a force affects an object, the object gains acceleration, proportional to its strength and inversely proportional to its mass."

Newton's Second Law Statement

Newton's second law of motion states that the force applied to the system is equal to the time rate of change of momentum.

So, F=dP/dt​

So, F=d(mv)​/dt

Or F=m(dv/dvt)

Acceleration, a, is defined as a change in velocity, meaning a change in its magnitude or direction, or both.

An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system.

Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

The weight w of an object is defined as the force of gravity acting on an object of mass . The object experiences an acceleration due to gravity g:

If the only force acting on an object is due to gravity, the object is in free fall.

Friction is a force that opposes the motion past each other of objects that are touching.

Newton's second law studies the movement of an object when external forces affect it. When a constant force affects a huge object, it causes it to accelerate, that is, to change its speed, at a constant rate.

In the simplest case, the force acting on an object at rest causes it to accelerate in the direction of the force. However, if the object is indeed in motion it may appear that the object is speeding up, slowing down, or changing its direction depending on the direction of force, directions taken by the object, and the frame of reference in which it is moving Relative to each other.

Mathematically, Newton's second law can be expressed through the following equation:

where F is the resultant force, m is the mass of the object, and a is the acceleration of the body.

This relationship applies the principle of preserving the momentum, which is that when the sum of the resultant forces acting on the object is equal to zero, the momentum of the object remains constant. The resultant force is equal to the rate of change in the momentum.

This law also means that when two equal forces act on two different bodies, the object with greater mass will have less acceleration and slower motion, and the object with less mass has greater acceleration. For example, to illustrate:

If we have two similar engines, one for a large car and the other for a small car, then the small one will have more acceleration because its mass is less and the large one will have less acceleration because its mass is greater.

You can try PraxiLabs virtual lab for online Physics experiments ... Subscribe now and select your plan

We always see the applications of Newton's second law of motion in daily life when:

like stopping a moving ball rolling on the ground.

Newton's second law of motion can be observed by comparing the acceleration produced in a car and a truck after applying an equal magnitude of force to both. It is easy to notice that after pushing a car and a truck with the same intensity, the car accelerates more than the truck. This is because the mass of the car is less than the mass of the truck.

Reducing the weight of racing cars to increase their speed , engineers try to keep vehicle mass as low as possible, as lower mass means more acceleration, and the higher the acceleration the greater the chances of winning the race.

For a rocket to leave the earth's orbit and enter outer space, a force called thrust is required. As per the second law of motion given by Sir Issac Newton, the force is proportional to the acceleration; therefore, to launch a rocket, the magnitude of thrust is increased, which in turn increases the acceleration. The speed achieved by the rocket finally helps it to escape the earth's gravitational field and enter space.

When we kick the ball we exert force in a specific direction, which is the direction the ball will move. In addition, the more forcefully the ball is kicked, the more force we apply to it and the further away the ball is.

During a car crash, there exists a force between the obstacle and the car, which is known as the impact force. The magnitude of the impact force depends on the mass of the objects involved in the collision and the speed with which the objects move. This means that the greater the mass of the objects involved in the collision, the more will be the intensity of the impact force. Similarly, the more the acceleration with which the car moves, the greater will be the magnitude of the impact force.

Of the two walking people, if one is heavier than the other, the one who weighs the heaviest walks slower because the acceleration of the one who weighs the lighter is more.

When an object is thrown from a certain height, the gravitational pull of the earth helps it to develop acceleration. The acceleration increases as the object advanced towards the earth. According to Newton's second law of motion, the acceleration developed by a body is directly proportional to the force. When the object hits the ground, the impact force comes into action. This is the reason why a brittle object thrown from a tall building suffers more deformity than the situation where the same object is thrown from a comparatively shorter building.

A karate player makes use of the second law of motion to perform the task of breaking a slab of bricks. Since, according to law, the force is proportional to the acceleration, the player tends to move his/her hands over the slab of bricks swiftly. This helps him/her to gain acceleration and produce a proportionate amount of force. The force is sufficient enough to break the bricks.

In simple terms, Newton's second law of motion states that if force is applied to any object that has mass, it will result in the production of an equivalent amount of acceleration in the object. For instance, when we turn on the ignition system of the car, the engine of the car produces sufficient force that enables the car to move with proportionate acceleration.

Newton's laws of motion form the basis for principles used in sport movements. Methods of training that depart from these laws would not make sense mechanically. Tips for efficient sport performances are built around these laws and principles.

Normally, baseball is at rest, It needs external force to move: gets thrown or is hit. The distance the ball travels depends on the amount of force that acts on it.

If a baseball player hits a ball with double the force, the rate at which the ball will accelerate (speed up) will be doubled

A ball develops a certain amount of acceleration after being hit. The acceleration with which the ball moves is directly proportional to the force applied to it. This means that the harder you hit the ball, the faster it will move, thereby demonstrating Newton's second law of motion in daily life.

A karate player makes use of the second law of motion to perform the task of breaking a slab of bricks. Since, according to law, the force is proportional to the acceleration, the player tends to move his/her hands over the slab of bricks swiftly. This helps him/her to gain acceleration and produce a proportionate amount of force. The force is sufficient enough to break the bricks.

Football players can slow down, stop, or reverse the direction of other players depending upon how much force they can generate and in which direction.

When we kick the ball we exert force in a specific direction, which is the direction the ball will move. In addition, the more forcefully the ball is kicked, the more force we apply to it and the further away the ball is.

Get Started Praxilabs For FREE

Law of Acceleration Examples in Real Life

It is easier to push an empty shopping cart than a full one, because the full shopping cart has more mass than the empty one. This means that more force is required to push the shopping cart.

Law of acceleration can be observed by comparing the acceleration produced in a car and a truck after applying an equal magnitude of force to both. It is easy to notice that after pushing a car and a truck with the same intensity, the car accelerates more than the truck.

(If you use the same force to push a truck and a car, the car will have more acceleration than the truck because the car has less mass.)

If a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.

Real Life Examples of Newton's Second Law

Riding your bicycle is a good example of this law of motion at work. Your bicycle is the mass. Your leg muscles pushing on the pedals of your bicycle is the force. When you push on the pedals, your bicycle accelerates. You are increasing the speed of the bicycle by applying force to the pedals.

When traveling in a car, when the car accelerates, we feel the back of our seat pushing us forward. The back of our seat operates force on our back which is proportional to the acceleration and our weight (mass).

When an object falls in a free fall onto the ground, it accelerates because the force of gravity of earth pulls it.
Which Technology Uses Newton's Second Laws of motion?
There are lots of technologies based on Newton's laws of motion. For example, Newton's second law of motion provides the foundation for much of the mathematics in engineering mechanics.

In the study of dynamics, engineers apply Newton's second law to predict the motion of an object experiencing a net force. Using the equation F = ma, engineers can model the position, velocity and acceleration of an object, or they can measure these values to learn about the forces acting on the object.

In the field of statics, engineers use Newton's second law to calculate forces acting upon stationary objects. Because a non-moving object's acceleration is zero, the forces acting on the object must sum to zero. For example, in designing structures, engineers apply Newton's second law in calculating the forces acting on joints in the framework of buildings and bridges.

How Can Newton's First Law of Motion Be Obtained from the Second Law of Motion?

When net force is zero and when moving with constant speed.

Newton's first law of motion states that a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.

If a body experiences an acceleration ( or deceleration) or a change in direction of motion, it must have an outside force acting on it. Outside forces are sometimes called net forces or unbalanced forces.

The second law of motion states that if an unbalanced force acts on a body, that body will experience acceleration (or deceleration), that is, a change of speed.

So, Outside forces are sometimes called net forces. If net force acting on a moving body is zero, the body will be at a constant velocity. Thus Newton's first law of motion can be obtained from the second law of motion.

How Does the First Law of Motion Lie in the Second Law of Motion?

Newton's first law of motion states that a body will stay at rest or continue its path with constant velocity unless an external force acts upon it.

Newton's second law of motion states that the net force that acts upon a body is equal to the mass of the body multiplied by the acceleration due to the net force. In other words, Fnet=ma.

Now, one can argue that Newton's second law of motion leads to the first law. Consider this: since Fnet=ma, with zero net force (no external forces), 0=ma.

Now, m is some finite positive value. In other words, this means that a=0. By definition, then, there is constant velocity (possibly constant zero velocity). Thus, it seems that Newton's second law of motion leads to the first law.

Why Is the Second Law of Motion the Most Important?

Newton's second law of motion F=ma is very important because it shows the relationship between forces and motion. It allows you to calculate the acceleration (and therefore velocity and position) of an object with known forces. This is incredibly valuable for scientists, engineers, inventors, etc.

What Are the Two Factors that Affect Newton's Second Law?

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

Praxilabs Virtual Labs in Mechanical Physics

virtual science labs enable you to conduct various laboratory experiments in physics, chemistry and biology online anytime and anywhere.

Create your free account and try now the virtual labs in mechanics that explain Newton's laws of motion and applications of newton's laws of motion in daily life.

Get started now with Praxilabs 3D virtual Labs!

# data[].attributes.attachment_link.title
Applications of Newton's Second Law of Motion - praxilabs

# data[].attributes.attachment_link.description
We always see the applications of Newton's second law of motion in daily life when we try to move an object like stopping a moving ball rolling on

# data[].attributes.attachment_link.readable_text
What is Newton's third law?

You probably know that the Earth pulls down on you. What you might not realize is that you are also pulling up on the Earth. For example, if the Earth is pulling down on you with a gravitational force of 500 N, you are also pulling up on the Earth with a gravitational force of 500 N. This remarkable fact is a consequence of Newton's third law.

Newton's third law: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.

This law represents a certain symmetry in nature: forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction.

We can readily see Newton's third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated below.

The swimmer pushes against the pool wall with her feet and accelerates in the direction opposite to that of her push. The wall has exerted an equal and opposite force back on the swimmer. You might think that two equal and opposite forces would cancel, but they do not because they act on different systems. In this case, there are two systems that we could investigate: the swimmer or the wall. If we select the swimmer to be the system of interest, as in the image below, then is an external force on this system and affects its motion. The swimmer moves in the direction of . In contrast, the force acts on the wall and not on our system of interest. Thus does not directly affect the motion of the system and does not cancel . Note that the swimmer pushes in the direction opposite to that in which she wishes to move. The reaction to her push is thus in the desired direction.

What are other examples of Newton's third law?

Other examples of Newton's third law are easy to find. As a professor paces in front of a whiteboard, she exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes her to accelerate forward.

Similarly, a car accelerates because the ground pushes forward on the drive wheels in reaction to the drive wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw rocks backward.

In another example, rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called thrust. It is a common misconception that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can more readily expel the exhaust gases.

Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and forward motion.

What do examples involving Newton's third law look like?

Example 1: Fridge push

A person drives a cart, Cart 1, to the right while pushing another cart, Cart 2, that has a massive refrigerator on it. The total mass of Cart 2, cart plus fridge, is three times the total mass of Cart 1, cart plus person. If the person is driving with enough force that the two carts accelerate to the right, what can be said for sure about the magnitudes of the forces on the carts?

Example 2: Third-law-force pairs

A box sits at rest on a table as seen in the image below. Various forces are listed in the table below the image.

Drag the forces in the right column so that they're lined up with their Newton's third law partner force in the left column.

# data[].attributes.attachment_link.title
What is Newton's third law? (article) | Khan Academy

# data[].attributes.attachment_link.description
What is Newton's third law? You probably know that the Earth pulls down on you. What you might not realize is that you are also pulling up on the Earth. For example, if the Earth is pulling down on you with a gravitational force of 500 N, you are also pulling up on the Earth with a gravitational force of 500 N.

# data[].attributes.headline
Short Article: Newton's Second Law of Motion

# data[].attributes.subject
Short Article: Newton's Second Law of Motion

# data[].attributes.attachment_link.readable_text
Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. Objects at equilibrium (the condition in which all forces balance) will not accelerate. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

The BIG Equation

Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

a = Fnet / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Fnet = m * a

In this entire discussion, the emphasis has been on the net force. The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is important to remember this distinction. Do not use the value of merely "any 'ole force" in the above equation. It is the net force that is related to acceleration. As discussed in an earlier lesson, the net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. If necessary, review this principle by returning to the practice questions in Lesson 2.

Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written.

1 Newton = 1 kg * m/s2

The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.

Your Turn to Practice

The F net = m * a equation is often used in algebraic problem solving. The table below can be filled by substituting into the equation and solving for the unknown quantity. Try it yourself and then use the click on the buttons to view the answers.

Net Force

(N)

Mass

(kg)

Acceleration

(m/s/s)

1.

10

2

2.

20

2

3.

20

4

4.

2

5

5.

10

10

Newton's Second Law as a Guide to Thinking

The numerical information in the table above demonstrates some important qualitative relationships between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant). Similarly, comparing the values in rows 2 and 4 demonstrates that a halving of the net force results in a halving of the acceleration (if mass is held constant). Acceleration is directly proportional to net force.

Furthermore, the qualitative relationship between mass and acceleration can be seen by a comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling of the mass results in a halving of the acceleration (if force is held constant). And similarly, rows 4 and 5 show that a halving of the mass results in a doubling of the acceleration (if force is held constant). Acceleration is inversely proportional to mass.

The analysis of the table data illustrates that an equation such as F net = m*a can be a guide to thinking about how a variation in one quantity might affect another quantity. Whatever alteration is made of the net force, the same change will occur with the acceleration. Double, triple or quadruple the net force, and the acceleration will do the same. On the other hand, whatever alteration is made of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or quadruple the mass, and the acceleration will be one-half, one-third or one-fourth its original value.

The Direction of the Net Force and Acceleration

As stated above, the direction of the net force is in the same direction as the acceleration. Thus, if the direction of the acceleration is known, then the direction of the net force is also known. Consider the two oil drop diagrams below for an acceleration of a car. From the diagram, determine the direction of the net force that is acting upon the car. Then click the buttons to view the answers. ( If necessary, review acceleration from the previous unit.)

In conclusion, Newton's second law provides the explanation for the behavior of objects upon which the forces do not balance. The law states that unbalanced forces cause objects to accelerate with an acceleration that is directly proportional to the net force and inversely proportional to the mass.

We Would Like to Suggest ...

Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Force Interactive. You can find it in the Physics Interactives section of our website. The Force Interactive allows a learner to explore the effect of variations in applied force, net force, mass, and friction upon the acceleration of an object.

Rocket Science!
NASA rockets (and others) accelerate upward off the launch pad as they burn a tremendous amount of fuel. As the fuel is burned and exhausted to propel the rocket, the mass of the rocket changes. As such, the same propulsion force can result in increasing acceleration values over time. Use the Rocket Science widget below to explore this effect.

Check Your Understanding

1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object.

2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s 2. Determine the mass of the encyclopedia.

3. Suppose that a sled is accelerating at a rate of 2 m/s 2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?

4. Suppose that a sled is accelerating at a rate of 2 m/s 2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?

# data[].attributes.attachment_link.description
Newton's second law describes the affect of net force and mass upon the acceleration of an object. Often expressed as the equation a = Fnet/m (or rearranged to Fnet=m*a), the equation is probably the most important equation in all of Mechanics.

# data[].attributes.attachment_link.readable_text
Why do objects slow down?

Before Galileo and Newton, many people thought objects slowed down because they had a natural built in tendency to do so. But those people weren't taking into account the many forces-e.g., friction, gravity, and air resistance-here on Earth that cause objects to change their velocity. If we could observe the motion of an object in deep interstellar space, we would be able to observe the natural tendencies of an object's motion free from any external influences. In deep interstellar space, we would observe that if an object had a velocity, it would continue moving with that velocity until there was some force to cause a change in the motion. Similarly, if an object were at rest in interstellar space, it would remain at rest until there was a force to cause it to change its motion.

In the video below, we can see that objects in the international space station either remain at rest or continue with constant velocity relative to the space station until acted upon by a force.

The idea that objects only change their velocity due to a force is encapsulated in Newton's first law.

Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.

Note the repeated use of the verb remains. We can think of this law as preserving the status quo of motion. Newton's first law of motion states that there must be a cause-which is a net external force-for there to be any change in velocity, either a change in magnitude or direction. An object sliding across a table or floor slows down due to the net force of friction acting on the object. But on an air hockey table, where air keeps the puck from touching the table, the air hockey puck continues moving with a roughly constant velocity until a force acts on it-like when it bumps into the side of the table.

What do force, external force, and net force mean?

An external force is a force originating from outside an object rather than a force internal to an object. For instance, the force of gravity that Earth exerts on the moon is an external force on the moon. However, the force of gravity that the inner core of the moon exerts on the outer crust of the moon is an internal force on the moon. Internal forces within an object can't cause a change in that object's overall motion.

In other words, if a box of frozen burritos had a force of magnitude 45 Newtons exerted on it to the right and a force of magnitude 30 Newtons exerted on it to the left, the net force in the horizontal direction would be

Assuming rightward is the positive direction.

Newton's first law says that if the net force on an object is zero (), then that object will have zero acceleration. That doesn't necessarily mean the object is at rest, but it means that the velocity is constant. In other words, constant zero velocity-at rest-or constant non-zero velocity-moving with a constant velocity.

For the box of frozen burritos, if the rightward force had a magnitude of 45 Newtons and the leftward force had a magnitude of 45 Newtons, the net force would be zero. The box of burritos would either continue moving with a constant velocity-if it started with a velocity before the forces were applied-or stay at rest-if it was already at rest before the forces were applied.

What does mass mean?

The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. Newton's first law is often called the law of inertia. As we know from experience, some objects have more inertia than others. It is obviously more difficult to change the motion of a large boulder than that of a basketball, for example.

The inertia of an object is measured by its mass. Mass can be determined by measuring how difficult an object is to accelerate. The more mass an object has, the harder it is to accelerate.

Also, roughly speaking, the more "stuff"-or matter-in something, the more mass it will have, and the harder it will be to change its velocity, i.e., accelerate.

What do solved questions involving Newton's first law look like?

Example 1: space probe drift

A space probe is drifting to the right at a constant velocity in deep interstellar space-far from any influence due to planets and stars-with its rockets off. If two rocket thrusters both turn on simultaneously exerting identical forces leftward and rightward in the directions shown, what would happen to the motion of the rocket?

a. The space probe would continue with constant velocity.
b. The space probe would speed up.
c. The space probe would slow down and eventually stop.
d. The space probe would immediately stop.

The correct answer is a. According to Newton's first law, a non-zero net force is required to change the velocity of an object. The net force on the space probe is zero-since the forces on it cancel-so there is no change in the velocity of the probe.

Example 2: elevator lift

An elevator is being pulled upward at a constant velocity by a cable as seen in the diagram below. While the elevator is moving upward at constant velocity, how does the magnitude of the upward force exerted on the elevator by the cable--compare to the magnitude of the downward force of gravity--on the elevator?

a. is greater than .
b. is equal to .
c. is smaller than .
d. could be larger or smaller than depending on the mass of the elevator.

The correct answer is b. If the elevator is moving with constant velocity, the net force must be zero. In order for the net force on the elevator to be zero, the upward and downward forces must cancel exactly.

Example 3: space probe path

A space probe is drifting to the right with constant velocity in deep interstellar space-far from any influence due to planets and stars. If a rocket thruster turns on and then off for a short burst of force in the direction shown, what would best represent the path traveled by the rocket after the thruster turns off?

The correct answer is c. After the rocket thruster turns off, there will be no net force on the space probe. Once the net force is zero, the velocity-both magnitude and direction-must be constant. Because of Newton's first law, the space probe moves in a straight line at constant speed. The fact that there was a vertical force on the space probe does not affect the horizontal velocity of the space probe, it only changes the vertical velocity. A constant vertical and horizontal velocity yields a diagonal straight line through space.

# data[].attributes.attachment_link.title
What is Newton's first law? (article) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.attachment_link.readable_text
This article was most recently revised and updated by

Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum or its direction or both. Newton's second law is one of the most important in all of physics. For a body whose mass m is constant, it can be written in the form F = m a, where F (force) and a ( acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it.

Newton's third law: the law of action and reaction

Newton's third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing problems of static equilibrium, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion. The forces it describes are real ones, not mere bookkeeping devices. For example, a book resting on a table applies a downward force equal to its weight on the table. According to the third law, the table applies an equal and opposite force to the book. This force occurs because the weight of the book causes the table to deform slightly so that it pushes back on the book like a coiled spring.

If a body has a net force acting on it, it undergoes accelerated motion in accordance with the second law. If there is no net force acting on a body, either because there are no forces at all or because all forces are precisely balanced by contrary forces, the body does not accelerate and may be said to be in equilibrium. Conversely, a body that is observed not to be accelerated may be deduced to have no net force acting on it.

Influence of Newton's laws

Newton's laws first appeared in his masterpiece, Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. In 1543 Nicolaus Copernicus suggested that the Sun, rather than Earth, might be at the centre of the universe. In the intervening years Galileo, Johannes Kepler, and Descartes laid the foundations of a new science that would both replace the Aristotelian worldview, inherited from the ancient Greeks, and explain the workings of a heliocentric universe. In the Principia Newton created that new science. He developed his three laws in order to explain why the orbits of the planets are ellipses rather than circles, at which he succeeded, but it turned out that he explained much more. The series of events from Copernicus to Newton is known collectively as the Scientific Revolution.

In the 20th century Newton's laws were replaced by quantum mechanics and relativity as the most fundamental laws of physics. Nevertheless, Newton's laws continue to give an accurate account of nature, except for very small bodies such as electrons or for bodies moving close to the speed of light. Quantum mechanics and relativity reduce to Newton's laws for larger bodies or for bodies moving more slowly.

The Editors of Encyclopaedia Britannica Erik Gregersen.

# data[].attributes.attachment_link.title
Newton's laws of motion - Momentum, Action-Reaction, Net Force

# data[].attributes.attachment_link.description
Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.

# data[].attributes.headline
Short Video: Newton's Third Law of Motion

# data[].attributes.subject
Short Video: Newton's Third Law of Motion

# data[].attributes.attachment_link.title
Newton's Third Law of Motion: Action and Reaction

# data[].attributes.headline
Short Video: Newton's Second Law of Motion

# data[].attributes.subject
Short Video: Newton's Second Law of Motion

# data[].attributes.headline
Short Video: Newton's First Law of Motion

# data[].attributes.subject
Short Video: Newton's First Law of Motion

# data[].attributes.attachment_link.title
Newton's First Law of Motion: Mass and Inertia

# data[].attributes.headline
Midlength Video: Newton's Laws of Motion

# data[].attributes.subject
Midlength Video: Newton's Laws of Motion

# data[].attributes.attachment_link.title
Contact Force Between Blocks With Kinetic Friction - Physics Problems & Examples

# data[].attributes.attachment_link.title
Contact Forces | Dynamics | AP Physics 1 | Khan Academy

# data[].attributes.attachment_link.readable_text
A gravitational field g at the location of an object with mass m causes a gravitational force of magnitude mg to be exerted on the object in the direction of the field.

Equation: F = mg

Weight, or force of gravity, is a force that acts on all objects near Earth. As pictured in the image above, Weight is always acting downwards towards the center of the Earth. The acceleration due to gravity on Earth, or g, is equal to 9.81 m/s/s; however, it is acceptable on the AP Physics 1 exam to substitute in 10 m/s/s for the acceleration due to gravity.

With this knowledge, you can use an object's mass in kilograms to find its weight utilizing the equation F = mg. If this is the only force exerted on an object, the object is said to be in free fall. If you recall from Kinematics, an object's acceleration is equal to 9.8 m/s/s when it is in free fall.

Key Concept: Weight - the Force of Gravity experienced by an object, changes depending on the relative location to Earth's surface or other planets

Key Concept: Mass - a measure of the inertia of an object, stays the same regardless of location

Weight is often confused with mass, but they are not the same thing. Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on an object due to gravity. The mass of an object remains the same no matter where it is, but its weight will change depending on the strength of the local gravitational field.

Here are some key points about weight and gravitational fields:

Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on an object due to gravity.

The mass of an object remains the same no matter where it is, but its weight will change depending on the strength of the local gravitational field.

A gravitational field is the region around a massive object in which other objects experience a force of attraction due to the mass of the first object.

The strength of a gravitational field is determined by the mass of the object and its distance from other objects.

The gravitational field of a planet or other celestial body extends throughout the universe, but the strength of the field decreases with distance from the object.

The gravitational field of the Earth is what gives objects their weight.

Example Problem #1:

A 5.00-kg object is placed on a frictionless table. Determine the gravitational force on the object due to Earth if the acceleration due to gravity is 9.8 m/s^2.

To solve this problem, you can use the equation F=mg, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. Plugging in the given values, we get:

F = (5.00 kg)(9.8 m/s^2) = 49 N

So the gravitational force on the object is 49 N. Keep in mind that this problem assumes that the object is at rest and is not moving. If the object is in motion, other forces may also be acting on it and you would need to take them into account in order to determine the total force acting on the object.

Example Problem #2:

A scientist is studying the behavior of a new type of material on different planets. She places a 10.0 g sample of the material on the surface of Planet X, which has a mass of 5.00 x 10^23 kg and a radius of 6.38 x 10^6 meters. The acceleration due to gravity on Planet X is 8.87 m/s^2. Calculate the gravitational force acting on the sample.

To solve this problem, we first need to determine the mass of the sample in kilograms. We can do this by using the formula m = m(g)/1000, where m(g) is the mass in grams and 1000 is the conversion factor from grams to kilograms. Plugging in the given value, we have:

m = (10.0 g)/1000 = 0.01 kg

Next, we can use the formula F = mg to calculate the gravitational force acting on the sample. Plugging in the values, we have:

F = (0.01 kg)(8.87 m/s^2) = 0.09 N

Therefore, the gravitational force acting on the sample is 0.09 N.

Example Problem #3:

A student is studying the weight of a textbook. The textbook has a mass of 2.00 kg and the acceleration due to gravity is 9.80 m/s^2. Calculate the weight of the textbook in newtons and in pounds.

To solve this problem, we can use the formula F = mg, where F is the weight of the object, m is the mass of the object, and g is the acceleration due to gravity. Plugging in the given values, we have:

F = (2.00 kg)(9.80 m/s^2) = 19.6 N

To convert the weight to pounds, we can use the conversion factor 1 N = 0.225 pounds. Plugging in the value for the weight in newtons, we have:

Weight (pounds) = (19.6 N)(0.225 pounds/N) = 4.42 pounds

# data[].attributes.attachment_link.title
The Gravitational Field - AP Physics 1 Study Guide 2024 | Fiveable

# data[].attributes.attachment_link.description
Cram for AP Physics 1 - Dynamics with Fiveable Study Guides. Includes key concepts, notes, vocab, and practice quizzes.

# data[].attributes.attachment_link.title
AP Physics 1: Universal Gravitation Review

# data[].attributes.attachment_link.title
Systems - AP Physics 1 Study Guide 2024 | Fiveable

# data[].attributes.attachment_link.description
Cram for AP Physics 1 – Dynamics with Fiveable Study Guides. Includes key concepts, notes, vocab, and practice quizzes.

# data[].attributes.attachment_link.title
Systems and Objects | Dynamics | AP Physics I | Khan Academy

# data[].attributes.attachment_link.title
How to Cram Dynamics in 1.5 hours (AP physics 1)

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.body
16%-20% exam score

# data[].attributes.body
12%-18% of exam score

# data[].attributes.body
For this unit and all other units check the previous tabs for materials you can use across units to quiz yourself and review. Sites like 'Albert' and 'Khan Academy' are linked there and can be very helpful.

# data[].attributes.headline
Quiz yourself (You don't have to download anything)

# data[].attributes.subject
Quiz yourself (You don't have to download anything)

# data[].attributes.attachment_link.title
Oops. Something went wrong. Please try again. | Khan Academy

# data[].attributes.attachment_link.description
We’ll get right to the point: we’re asking you to help support Khan Academy. We’re a nonprofit that relies on support from people like you. If everyone reading this gives $12 monthly, Khan Academy can continue to thrive for years. Please help keep Khan Academy free, for anyone, anywhere forever.

# data[].attributes.attachment_link.title
How to Cram Kinematics in 1 hour for AP Physics 1

# data[].attributes.body
Join our Discord community to chat about AP Physics 1 with fellow test takers.

# data[].attributes.attachment_link.description
Check out the StudyCrew community on Discord - hang out with 56 other members and enjoy free voice and text chat.

# data[].attributes.body
Send an email to apphysics.learningpath@gmail.com and we'll do our best to respond to any questions regarding AP Physics 1.

# data[].attributes.body
Topics Covered: Rotational kinematics, dynamics, and static equilibrium.

Key Concepts: Torque, rotational inertia, angular momentum, equilibrium, and rotational kinematics and energy.

# data[].attributes.body
Topics Covered: Simple harmonic motion, mechanical waves, and sound.

Key Concepts: Mass-spring systems, pendulums, wave properties (such as wavelength, frequency, speed), sound properties, and the Doppler effect.

# data[].attributes.body
Topics Covered: Linear momentum and collisions.

Key Concepts: Impulse, conservation of momentum in collisions (elastic and inelastic), and center of mass.

# data[].attributes.body
Topics Covered: Work, energy, and power.

Key Concepts: Kinetic energy, potential energy (gravitational and elastic), work-energy principle, conservation of energy, and power

# data[].attributes.body
Topics Covered: Circular motion, gravitational forces.

Key Concepts: Uniform circular motion, centripetal force, Newton's law of universal gravitation, and the motion of satellites.

# data[].attributes.body
Topics Covered: Forces and Newton’s laws of motion.

Key Concepts: Inertia, the relationship between force, mass, and acceleration, tension, friction, and the concept of net force.

# data[].attributes.body
Topics Covered: Motion in one dimension, vectors and motion in two dimensions.

Key Concepts: Displacement, velocity, acceleration, projectile motion, and freefall.