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Notes for IB Physics topic 9. ONLY FOR HL!

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Notes covering IB Physics electricity and magnetism (topic 5). Sometimes a reference to a page in the Oxford IB Physics textbook might be given instead of a note - this is because the concept wasn't considered worth writing down (too trivial or too long).

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ib physics "ib physics" "ap physics" "high school physics" "university physics" science "jee practice"

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Many IB Physics students have written me to tell me of their success using the videos. The videos contain many worked examples and intuitive explanations. Here is the testimony of one student, "I would just like to say a massive thank you to you for uploading your videos.

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Equations that aren't on the data booklet

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Equations that aren't on the data booklet

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The formulae below are not in the IB physics data booklet and you should memorise them!

You should also make sure you have a copy of the IB physics data booklet and that you practise using it before your exams.
Download your copy of the IB Physics Data Booklet HERE
Now for the important part...

I'll walk through each topic and explain each equation that needs to be memorised.

Topic 1: Measurements and Uncertainties

One of the basic error propagation rules is not included. This is if you are multiplying a quantity by a constant factor with no associated error, then the absolute error is multiple by the constant too. However, the relative error omits the constant.

All of the other formulae needed for manipulating errors are included in the data booklet.

Topic 2: Mechanics

For an object in freefall in a gravitational field, the total energy in the system is (assuming no air resistance or drag):

Power in terms of work done:

Topic 3: Thermal Physics

The Stefan-Boltzmann constant (k), the universal gas constant ( R) and Avogadro's number (N) are all linked by:

Topic 4: Waves

Intensity of electromagnetic radiation at a distance r from a source with power, P.

Topic 5: Electricity and Magnetism

Another expression for the formula for internal resistance is:

Topic 6: Circular Motion and Gravitation

Average angular velocity is equal to the rate of change of angular displacement, θ, with respect to time, t.

Topic 7: Atomic, Nuclear & Particle Physics

Example of an alpha decay

Example of a beta decay

Topic 8: Energy Production

If a wind turbine has a blade radius, r, then the area, A, swept our by the blades is πr² and the maximum theoretical kinetic energy arriving at the turbine every second (and hence the maximum theoretical power) is:

This assumes that all the kinetic energy of the wind can be used, which is not possible given that the wind will move out of the back of the turbine after moving the blades and will hence retain some of its kinetic energy.

Topic 9: Wave Phenomena

The defining equation of SHM is:

Topic 10: Fields

You can find the relative permittivity (ε) in terms of the permittivity of the medium (ε) and vacuum (ε) is:

The potential difference between two parallel plates, with voltage, V, and separation, d, is:

Topic 11: Electromagnetic Induction

Maximum and minimum values for an emf in an ac generator is:

Topic 12: Quantum and Nuclear Physics

de Broglie states that particles have wave-like properties and they are linked by the following equation:

Where λ is the wavelength, h is the planck's constant and p is the momentum of the particle ( p=mv)

If you memorise the formulae listed above NOT listed in the IB physics data booklet you will be well on the way to achieving a 7 in your IB physics exam! You might also want to:

Hope this helps!

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Formulae NOT in the IB Physics Data Booklet (Memorise These!)

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The formulae below are not in the IB physics data booklet and you should memorise them! You should also make sure you have a copy of the IB physics data booklet and that you practise using it before your exams. Download your copy of the IB Physics Data Booklet HERE Now for the important part...

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See the guide for this topic.

6.1 - Circular motion

Period, frequency, angular displacement and angular velocity

Uniform circular motion refers to circular motion at constant speed.

In a uniform circular motion, speed is constant while (angular) velocity and (angular) acceleration are constantly changing.

While the magnitude of its velocity remains constant, the direction of its velocity is constantly changing.

The acceleration causing this change in velocity is always directed towards the center of the circular path.

The period is the time taken for the object to complete one full circle and is usually calculated in seconds. The frequency can be calculated by 1/period and is usually measured in Hz.

Centripetal force is the corresponding force (resultant force) which causes the centripetal acceleration.

Properties:

Direction: Pointing towards the center of the circle / perpendicular to the instantaneous velocity

Magnitude:

Work done by centripetal force = 0

Centripetal force is not a type of force; rather, it is just the name we give to the net force causing a circular motion. For example:

The acceleration which gives rise to a circular motion is called the centripetal acceleration. Its magnitude is given by

It is directed towards the center of the circular motion and is perpendicular to the instantaneous velocity of the object.

6.2 - Newton's law of gravitation

The gravitational force between two objects can be calculated using Newton's universal law of gravitation

The gravitational field strength at a point is the force per unit mass experienced by a test mass at that point.

The gravitational field strength (g) due to an object is given by

Gravitational field strength at the surface of a planet

The gravitational field strength at the surface of a planet can be calculated by using the equation for gravitational field strength and substituting M and r by the mass and the radius of the planet respectively.

If we calculate the gravitational field strength at the surface of the Each using the mass and the radius of the Earth, we would obtain the value 9.81m/s^2, which is equal to the acceleration due to gravity on the surface of the Earth.

Different planets have different radii and masses. Consequently, different planets have different gravitational field strengths.

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Topic 6: Circular motion and gravitation

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See the guide for this topic. Period, frequency, angular displacement and angular velocity Uniform circular motion refers to circular motion at constant speed. In a uniform circular motion, speed is constant while (angular) velocity and (angular) acceleration are constantly changing. While the magnitude of its velocity remains constant, the direction of its velocity is constantly changing.

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Revision notes for IB Physics circular motion (topic 6)

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Topic 6 - Circular motion and gravitation

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Topic 6 - Circular motion and gravitation

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See the guide for this topic.

4.1 - Oscillations

Oscillations are periodic motions which center around an equilibrium position.

Simple harmonic motion (SHM) is a special type of oscillation. For example:

The simple pendulum

The vibration of strings in a violin

The spring-mass system, where the mass is initially displaced to produce a periodic motion around the equilibrium position

An object undergoes SHM if it experiences a force which is proportional and opposite of the displacement from its equilibrium position.

The period is independent of the amplitude of the SHM and can be given by the following equation

for a pendulum

and

for a spring-mass system

Time period, frequency, amplitude, displacement and phase difference

Displacement (x)

Amplitude

Period (T)

Frequency (f)

Phase difference

Displacement of the oscillating object at a specific time from its equilibrium position

Maximum displacement of the oscillating object

Time taken for one complete oscillation (in seconds)

Number of times the object oscillates per unit time (usually one second)

f=1/T

The difference between two SHMs with the same frequency in terms of their relative position in a cycle measured in radian

Conditions for simple harmonic motion

When the body is displaced from equilibrium, there must exist a restoring force (a force that wants to pull the body back to equilibrium).

The magnitude of the restoring force must be proportional to the displacement of the body and acts towards the equilibrium.

4.2 - Travelling waves

A travelling wave is a continuous disturbance in a medium characterized by repeating oscillations. For example:

A rope that is flicked up and down continuously creates a repeating disturbance similar to the shape of a sine/cosine wave.

Energy is transferred by waves.

Matter is not transferred by waves.

The direction of a wave is defined by the direction of the energy transfer.

Wavelength, frequency, period and wave speed

Wavelength, frequency, and period follow the same rules of SHM.

Wave speed can be calculated by the following equation

Transverse and longitudinal waves

Transverse wave

Longitudinal wave

The direction of oscillation is perpendicular to the direction of the wave

The direction of oscillation is parallel to the direction of the wave

Example:

Ÿ Water waves

Ÿ Wave in a string flicked up and down

Ÿ Light (electromagnetic waves)

Example:

Ÿ Wave produced in a spring

Ÿ Sound waves

Ÿ Earthquake P-waves

Transverse wave

Longitudinal wave

A point with maximum positive displacement is called a crest.

A point with minimum displacement is called a trough.

A region where particles are closed to each other is called a compression.

A region where particles are furthest apart from each other is called a rarefaction.

The nature of electromagnetic waves

All EM waves travel in vacuum at the same speed of 3*10^8m/s.

EM waves are transverse waves.

The speed of sound in 20 degrees Celsius dry air is approximately 343.2m/s.

Sound waves are longitudinal waves.

4.3 - Wave characteristics

Wavefronts:

Lines joining points which vibrate in phase.

Can be straight lines or curves.

The distance between successive wavefronts is the wavelength of the wave.

Rays:

Lines which indicate the direction of wave propagation.

Rays are perpendicular to wavefronts.

The amplitude and intensity of a wave depends on its energy.

The intensity of a wave is proportional to the square of its amplitude (I∝A^2).

Transverse and longitudinal waves

See previous section with the same title.

The principle of superposition states that the net displacement of the underlying medium for a wave is equal to the sum of the individual wave displacements.

The left shows constructive interference (superposition) where the two waves add up (e.g. 1+1=2). The right shows deconstructive interference (superposition) where the two waves cancel each other (e.g. 1+(-1)=0).

Light is a transverse wave (polarization only occur to transverse waves).

The polarization of light refers to the orientation of the oscillation in the underlying electric field.

Light is plane polarized if the electric field oscillates in one plane.

Left shows unpolarized light and right shows polarized light.
Polarization by reflection
When light is transmitted across a boundary between two mediums with different refractive indexes, part of the light is reflected and the remaining part is refracted (for further explanation, see section 4.4).

The light reflected is partially polarized, meaning that it is a mixture of polarized light and unpolarized light.

The extent to which the reflected light is polarized depends on the angle of incidence and the refractive index of the two mediums.

The angle of incidence at which the reflected light is totally polarized is called the Brewster's angle (ϕ) given by the equation

where n1 and n2 are the refractive indexes for their respective mediums

When the angle of incidence is equal to Brewster's angle, the reflected ray is totally polarized and the reflected ray is perpendicular to the refracted ray.
Polarizers and Analyzers
Polarizer:

A polarizer is a sheet of material which polarizes light.

When unpolarized light passes through a polarizer, its intensity is reduced by 50%.

Analyzer:

When polarized light passes through a polarizer, its intensity will be reduced by a factor dependent on the orientation of the polarizer. This property allows us to deduce the polarization of light by using a polarizer.

A polarizer used for this purpose is called an analyzer.

Malus' Law relates the incident intensity and transmitted intensity of light passing through a polarizer and an analyzer.

where I is the transmitted intensity, I0 is the initial light intensity upon the analyzer, θ is the angle between the transmission axis and the analyzer.

When light passes through an optically active substance, the plane of polarization rotates.

4.4 - Wave behaviour
Reflection
Angle of incidence = Angle of reflection

Reflection of waves from a fixed end is inverted.

Reflection of waves from a free end is not inverted.
Refraction
Refraction is the change in direction of a wave when it transmits from one medium to another.

The angle of incidence and the angle of refraction can be determined by Snell's law given by the following formula

where n1 and n2 are the refractive indexes for their respective mediums

Fast-to-slow: towards normal; slow-to-fast: away from normal

In addition, the refractive index n1 and n2 are related by the following equation

where v1 and v2 are the speed of the waves in their respective mediums and λ1 and λ2 are the wavelength of the waves of their respective mediums

Snell's law, critical angle and total internal reflection

See previous section (Reflection and refraction) for Snell's law.

The refractive index and the critical angle are related by the following equation Total internal reflection only occurs when the light ray propagates from a optically denser medium to an optically less dense medium.

Diffraction through a single-slit and around objects

Diffraction through a single-slit

Single-slit equations are not required for the standard level course.

Diffraction around objects

Maximums form at constructive interference (the maximum is shown by 1-2) and minimums form at deconstructive interference (the first minimum is shown by 3-4).

Like single-slit diffraction, double-slit diffraction occurs via the same methods of interference and has a similar diffraction pattern.

4.5 - Standing waves

Standing waves (stationary) waves result from the superposition of two opposite waves which are otherwise identical.

Energy is not transferred by standing waves.

A wave hits a wall and is reflected identically opposite.

The black wave shows the wave created by the superposition of the blue and green waves.

Air particles can oscillate and create standing waves in pipes with open or closed ends.

Antinodes are positioned at open ends and nodes are positioned at closed ends.

Standing waves on a string is equivalent to that in a pipe which is closed on both ends (nodes-node).

The following table summarizes the behavior of standing waves in pipes and strings:

Positions along the wave which are fixed are called nodes (minimum) and those with the largest displacement are called antinodes (maximum).

For standing waves, the distance between adjacent nodes = the distance between adjacent antinodes = λ/2.

Difference between standing waves and travelling waves

Standing waves

Travelling waves

Ÿ No energy is propagated along a standing wave

Ÿ A standing wave has nodes and antinodes

Ÿ The amplitude of the standing wave varies along the wave

Ÿ Particles between two adjacent nodes oscillate in phase and particles separated by exactly one node oscillate in antiphase.

Ÿ Energy is propagated in a travelling wave

Ÿ A travelling wave has neither nodes nor antinodes

Ÿ The amplitude of the travelling wave is constant throughout the wave

Ÿ The phase difference between two particles of a travelling wave can take any value between 0 and 2π

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See the guide for this topic. Oscillations are periodic motions which center around an equilibrium position. Simple harmonic motion (SHM) is a special type of oscillation.

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Notes covering IB Physics waves (topic 4).

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See the guide for this topic.

2.1 - Motion

A scalar quantity which measures how far two locations are apart from each other along a certain path.

A vector quantity defined by the length and direction of the line segment joining the initial and final positions of an object.

Velocity is a measure dependent on the motion of the observer. The relative velocity of A to B is equal to the vector subtraction of the velocity of B from the velocity of A.

Acceleration due to gravity of any free-falling object is given by g=9.81m/s^2. This value does not depend on the mass of the object.

Take note that acceleration is a vector and thus has a direction. If we assume the upwards direction to be positive, the acceleration due to gravity would have a negative value of g=-9.81m/s^2.

Displacement-time graph

The slope gradient indicates the velocity.

Straight lines imply constant velocity.

Velocity-time graph

The slope gradient indicates the acceleration.

Straight slanted lines imply constant acceleration or deceleration.

The area under the lines indicates the change in displacement.

Acceleration-time graph

Horizontal lines imply constant acceleration.

The area under the lines indicates the change in velocity.

Equations of motion for uniform acceleration

If acceleration is constant (uniform), the following equations can be used

An object is said to undergo projectile motion when it follows a curved path due to the influence of gravity.

If we assume air resistance to be negligible in a projectile motion:

The horizontal component of velocity is constant

The vertical component of velocity accelerates downwards at 9.81m/s^2

The projectile reaches its maximum height when its vertical velocity is zero

The trajectory is symmetric

The presence of air resistance changes the trajectory of the projectile by the following

The maximum height of the projectile is lower

The range of the projectile is shorter

The trajectory is not symmetric

Fluid resistance and terminal speed

Air resistance limits the maximum velocity an object could attain from free-falling. For example:

If you jump out of a plane and undergo free-falling, you will feel an upward force exerted on you by the surrounding air due to air resistance.

As you fall faster and faster due to gravity, this upward force exerted by air becomes greater and greater until it balances your weight. At this point, the net force acting on you becomes zero, and you no longer accelerate.

This specific velocity at which you stop accelerating during a free-fall is called the terminal velocity.

2.2 - Forces

Forces change the velocity or shape of objects.

The unit of force is newton (N).

Objects are represented as a point mass to enable the representation for forces as arrows in free-body diagrams.

On a free body diagram, forces acting on an object are represented as arrows which stem from a point mass.

The length and direction of the arrows corresponds to the magnitude and the direction of the forces acting on the body of interest.

Determining the resultant force

1. Resolve all acting forces into horizontal and vertical components

2. Add up the horizontal components

3. Add up the vertical components

4. Combine the sum of horizontal components and the sum of vertical components

A body is said to be in translational equilibrium if it the net force acting on the body is zero. This means the body is either at rest or travels at constant velocity. For example:

Mass hanging at rest

Elevator moving upwards at constant velocity

Parachutist reaching terminal velocity

Newton's First Law (Law of Inertia) states that a body remains at rest or travels with constant speed along a straight line unless acted upon by an external force. (Net force = 0)

Newton's Second Law states that net force is directly proportional to acceleration and to mass. (F=ma)

Newton's Third Law states that if a body A exerts a force on body B, then body B exerts a force of the same magnitude but in the opposite direction of body A.

This pair of forces is called an action-reaction pair, which must act on two different bodies.

Friction is a non conservative force which opposes motion. If there is no motion, then there will be no force caused by friction.

For two solid surfaces moving over each other, the friction will be affected by the nature (roughness etc) of the two surfaces. However, the surface area and velocity of the object does not affect the friction.

There are also two types of friction for solid surfaces: static friction and kinetic friction. Static friction is that which stops objects from beginning to move. Kinetic friction is that which slows objects down when they are moving. Static friction is always larger than kinetic friction.

These two types of friction are defined individually by their constants µs and µk respectively.

The forces of friction are also dependent on the normal force the surface is applying, leading to Friction force (static) =< µs * Normal force for objects that are not moving and Friction force (static) = µs * Normal force for objects that are moving.

​2.3 - Work, energy and power

Kinetic energy (KE) is the energy of a body due to its motion and is given by the equation

The gravitational potential energy (GPE) of an object changes with its height and is given by the equation

Elastic energy is potential energy stored as a result of the deformation of an elastic object such as the stretching of a spring and is given by the equation

Work done measures the transfer of energy due to a force and is a scalar quantity.

The work done W by a force F on an object is given by the equation

In a force-displacement graph, work done is the area under the curve.

Power (P) is the work done or the energy output per time given by the equation:

For constant force acting on an object with constant velocity, the power is given by the equation: P=Fv.

Principle of conservation of energy

Energy can neither be created nor destroyed; it can only be changed from one form to another. For example:

An electrical heater transforms electrical energy to thermal energy.

A falling object transforms potential energy to kinetic energy.

Total energy of an isolated body remains constant. In other words, ΔKE+ΔPE=0

Efficiency is the ratio of useful energy output to energy input as a percentage given by the equation

​2.4 - Momentum and impulse

Newton's second law expressed in terms of rate of change of momentum

The linear momentum (p) is given by the equation

The linear momentum (p) is a vector with the same direction as the velocity of an object.

The change of momentum of an object is called impulse.

Rearranging the formula describing Newton's second law results in the following expression

Impulse is given by the area of a force-time graph.

The law of conservation of linear momentum states that the sum of initial momentum is equal to the sum of final momentum in a closed system and can be given by the equation

Elastic collisions, inelastic collisions and explosions

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See the guide for this topic. A scalar quantity which measures how far two locations are apart from each other along a certain path. A vector quantity defined by the length and direction of the line segment joining the initial and final positions of an object.

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Notes covering mechanics (topic 2) of IB Physics. It is not recommended to study mechanics purely from those notes, they should be used as a reference or quick reminder.