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Circular motion is the movement of an object along the circumference of a circle. The rate that an object rotating spins is angular velocity, which describes the amount an angle changes per unit of time. Angular speed is measured in radians per second, and one radian is roughly 57.3o. Another part of circular motion is centripetal acceleration and force. This is when the acceleration or force is perpendicular to an object's velocity, causing it to move in a circle around a central point. Centrifugal force, a fake force opposite to centripetal force, is the sensation of being pulled towards the center rather than pushed out. This is caused by inertia and in reality we are feeling is the reaction force of our bodies resisting the centripetal force.

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ω=Δθ/Δt
This equation finds angular velocity by dividing the change in the angle by the change in time.

v=ωr
This equation is used to solve for linear velocity by multiplying the angular velocity by the radius.

a c=v t 2 / r
This equation is the tangential velocity squared divided by the radius. This yields the centripetal acceleration.

F c=mv t ² / r
This equation combines the centripetal acceleration and Newton's second law to find centripetal force.

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Newton's Laws are three laws of motion that explain how objects move when acted upon by forces. The first law states that an object at rest or in motion remains in its identical state unless acted upon by a net force, known as inertia. This means that if the net force is equal to zero, then the acceleration is also zero, and vice versa. The second law states that the acceleration of an object equals the force applied divided by the mass of the object. The more force applied, the greater the acceleration. The third law states that exchanges in forces are caused by the interaction of two objects.

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F=ma
This is the equation for net force when given the mass and acceleration.

a=F/m
This is the equation for acceleration when given force and mass.

m=F/a
This is the equation for mass when given the force and acceleration.

v=v ₀+at / x=x ₀+v0t +(1/2)at ²
These equations are used to find velocity and position when given mass and net force.

F net=F ₁ + F ₂...
This equation is used to find the net force when given all other forces acting upon an object.

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A 250 g ball traveling at 40 m/s to the right is hit with a racquet, which applies a force of 3,000 N to the left for 0.005 s. What is the velocity of the ball afterward?

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https://drive.google.com/file/d/1pQp2ce5AAlVMe0R56apePl0hSq7cADYo/view?usp=sharing

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Newton's laws can be seen in every aspect of life, and the movement of all things follow these laws. For example, if you roll a ball on the ground the ball eventually stops. This is because friction acts upon the ball and the net force decreases until it reaches zero, which is when it stops. The second law can be seen when pushing a wheelbarrow. The more force you use, the faster it accelerates. An example of the third law is throwing a ball. When you apply force to throw a ball, it pushes back against your hand.

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A race car is moving with a speed of 200 km/h on a circular section
of a race track that has a radius of 400 m. The race car and driver
have a mass of 1400 kg.

a) What is the magnitude of the centripetal acceleration felt

by the driver?
b) What is the centripetal force acting on the mass?

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https://drive.google.com/file/d/1FMExr4Toyz0CYfYLaBuoBzyqzopJRmN5/view?usp=sharing

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One example of circular motion is a bike tire. They rotate around a central axel and if you measure the rotations, you can find the linear velocity of the tires. You now know how fast the bike is going based off of the tires. Another example is when you turn on a curve while driving. When you turn, you are being pushed towards the central point of the arc of your turn.

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Static equilibrium is when the net force is equal to zero. For something to be in static equilibrium and at rest all forces must equal zero and all torque around any center of rotation must also be zero. This information can be used to calculate the torque or force on a given object or to ensure that something is stable.

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∑F =0
This summation equation is the sum of all forces equal zero. This is one of two conditions for static equilibrium. The unit for torque is Newton meters.

τ=F x r
This equation solves for torque by multiplying force by the distance from center to line of action.

∑τ=0
This equation is the sum of all torques should equal zero. This is the second of the conditions for static equilibrium.

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You have a balance beam of length 2 m with negligible mass. The fulcrum is 0.75 m from the left end. There is a 5 kg weight hanging 0.5 m from the left end, a 2 kg weight hanging 0.25 m from the right end, and a 6 kg weight hanging 0.75 m from the right end. You have a spare 5 kg weight. Where would you hang it to balance the beam?

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https://drive.google.com/file/d/14AuQpsqjpDT7PaZmy3kx4JLnopGQNLZy/view?usp=sharing

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One example of static Equilibrium in the real world is architecture. An architect must make sure the net force is zero in order for a building to be structurally sound.

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Momentum is a property of an object in motion that expresses an object's tendency to stay in motion. The greater the mass or velocity of an object the higher the momentum. Momentum can be thought of as the force that would have to be overcome in order for an object to stop. It is also a vector, and as a vector it can be positive or negative based on the direction. Momentum is measured in kilogram meters per second. Impulse is the change in an object's momentum, the product of force, and the period of time the force is being applied.

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p=mv
This equation solves for momentum by multiplying the mass times the velocity.

F=Δp / Δt
This equation solves for the force using the change in momentum divided by the change in time.

J=Δp=FΔt

This equation uses the change in momentum or the change in time multiplied by the force to find the impulse. This equation is a deviation of the previous equation.

J=Δp=p f−p i

This equation is similar to the one above in that it uses the change in momentum to calculate the impulse.

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A wind-up toy car has a mass of 66 g. The car is wound, and then released, going from being at rest to a constant velocity of 0.8 m/s. If the internal force of the winding on the tires is 0.1 N, what is the duration of the impulse imparted by the winding on the car.

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https://drive.google.com/file/d/1AH8SEyOImSOFn4PxAlU2tTrDn219xm7g/view?usp=sharing

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Momentum is everywhere and can be seen in a number of ways. One example is driving a car. If a small car that wasn't going very fast crashes, the damage isn't as sever as a larger vehicle going faster. This is because the small car has less momentum and less damaging force is required to stop it. An example for impulse is playing soccer. When the ball is coming towards you, it has momentum. When you kick it, for a very short amount of time you are exerting force on the ball, changing its momentum towards another direction.

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Acceleration is used in a wide variety of physics concepts. Acceleration itself is the rate at which velocity changes and the unit that goes with acceleration is meters per second squared. Acceleration can be positive or negative, with positive acceleration being an increase in speed and negative decreasing. Gravity is a form of acceleration and falling objects accelerate until they reach terminal velocity. Acceleration is an essential aspect of calculating forces. It is also used in kinematic equations to find either a distance, velocity, or time.

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a=Δv / Δt
This equation finds the acceleration when given the changes in time and velocity.

Δv=a / Δt
This equation is an adaptation of the previous one. Its used to find the change in velocity when given the acceleration and change of time.

v=v 0 + at
Acceleration is used in this equation to find either the initial velocity, final velocity, or time.

x f=x ₀ +v ₀ t + (1/2)at ²
This kinematic equation uses acceleration and other measures to find one of the variables without needing the final velocity.

v ²=v ₀ ² + 2a(x f - x ₀)
This kinematic equation uses acceleration and the other measures to solve for one of the variables without needing the time.

F=ma
This equation multiplies acceleration by the mass to find force

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What is the average acceleration of a cheetah that starts at rest and 3 s later is moving at a speed of 27 m/s? Is the acceleration greater or less than the acceleration of a $100,000 sports car that can go from 0 to 60 mph in 4 s?

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https://drive.google.com/file/d/101lFZu0H3pG9K7mCl7_h4mD9h5_SsjOp/view?usp=sharing

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One example of acceleration is driving a car. If I'm stopped at a stop sign and I push down on the gas, my car starts to accelerate forward. My speed increases by the number of meters of acceleration per second. Once I reach the speed limit, I stop accelerating and then the acceleration is zero. Knowing how to calculate acceleration can enable someone to figure out how much they need to accelerate if they want to reach a certain speed at a specific time.