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# AS-Level Physics Formula Sheet

Equations are crucial to solving physics questions and there are an enormous number of them. A list of formulae is included in a-level physics exams, so there is no need to remember them all. However, to be able to use these equations they need to be understood, what do the symbols mean and when can the equation be applied? On this formula sheet each equation is listed and then briefly explained. The following formulas are specifically for the AQA physics specification but the topics are similar between different specifications. Where needed, units are shown in square brackets e.g. *Length* [m].

## Important values

*c - Speed of light in a vacuum = 3 × 10 ^{8 }*[m/s]

*e - Charge of the electron = 1.6 × 10 ^{-19 }*[C]

*g - Gravitational acceleration (on Earth) = 9.81 *[m/s^{2}]

*h - Planck's constant = 6.63 × 10 ^{-34 }*[Js]

*1 *MeV* = 1.6 × 10 ^{-13 }*J

## Particle Physics

Antiparticles have the same rest energy.

Leptons are elementary particles.Hadrons aren't elementary particles, they are made up of quarks. Hadrons are either baryons or mesons.

Mesons are made up of a quark and an antiquark.

Baryons are made up of three quarks.

## Properties of quarks

u, d and s are the symbols for up, down and strange type quarks.

Anti-quarks have the opposite sign e.g. the anti-up quark has a charge of -2/3 e and a baryon number of -1/3.

Proton composition, p = uud.Neutron composition, n = udd.

## Properties of leptons

Total lepton number is conserved in particle interactions.

The lepton numbers for the electron family of particles and muon family of particles are conserved separately as well.

## Photons and energy levels

*photon energy,*

Energy of a photon[J]= Planck's constant × Frequency of the photon[Hz]

= Planck's constant × Speed of light in a vacuum ÷ Wavelength of the photon[m]

*photoelectricity,*

Energy of incoming photon[J]= Work function of metal[J]+ Maximum possible kinetic energy of outgoing photoelectron[J]

The work function is the minimum energy required to extract an electron from the metal.It can take more energy to extract the electron and hence the kinetic energy will be less than the maximum.

*energy levels,*

Energy of emitted photon[J]= Initial atomic energy level[J]- Final atomic energy level[J]alternatively,

Energy of absorbed photon[J]= Final atomic energy level[J]- Initial atomic energy level [J]

This equation is a statement of discrete energy levels for atoms, the energy of the photon has to be exactly equal to the difference between energy levels for it to be absorbed/emitted.

*de Broglie wavelength,*

de Broglie wavelength of particle[m]= Planck's constant[kgm/s]÷Momentum of particle

= Planck's constant[kg]÷ (Mass of particle× Velocity of the particl[m/s]e)

Particles (including light) exhibit properties of particles and waves, this is known as wave-particle duality.

## Waves

*wave speed,*

Wave speed[m/s]= Frequency of the wave[Hz]× Wavelength of the wave[m]

Wavelength is the distance between successive peaks of a wave.

Frequency is the number of oscillations per unit time.

*period,*

Frequency[Hz]= 1 ÷ Time period[s]

The time period of a wave is the time to complete one oscillation.

*first harmonic,*

Fundamental frequency of a string[Hz]= (1/2[m]÷ Length of the string)[N]×Square root(Tension in the string÷ Mass per unit length of the string[kg/m])

A standing wave is the superposition of two waves moving in opposite directions.The fundamental frequency (or "first harmonic") is the lowest frequency possible for a standing wave.

*fringe spacing,*

Fringe spacing[m]= Wavelength of light[m][m]× Distance separating doubles slits and the screen÷Slit separation[m]

This equation describes Young's double slit experiment. The experiment produces a repeating pattern of equally spaced dark bands and bright bands.The fringe spacing is the separation between successive bright bands (or equivalently the separation between successive dark bands).

*diffraction grating,*

Slit spacing[m][m]× Sine of the diffraction angle = Order of diffraction× Wavelength of light

A diffraction grating produces widely separated bright fringes. The order of diffraction is as shown below.

*refractive index of a substance,*

Refractiveindexof substance = Speed of light in a vacuum÷ Speed of light inside the substance

*law of refraction (Snell's law),*

Sine of angle of incidence = Refractive index of outgoing mediumRefractive index of incident medium ×Sine of angle of refraction×

Refraction occurs when light passes through a boundary between two materials with different refractive indices. The light enters from the incident medium and leaves through the outgoing medium.

All angles are measured from the normal (a line perpendicular to the surface of the boundary).

*critical angle,*

Sine of critical angle = Refractive index of outgoing medium÷ Refractive index of incident medium

For angles of incidence larger than the critical angle total internal reflection occurs.

## Mechanics

*moments,*

Moment about a turning point[Nm]= Force[N][m]× Perpendicular distance between turning point and the line of action of the force

A moment is the turning effect of a force.

For an object in equilibrium, the sum of anticlockwise moments about a tuning point is equal to the sum of clockwise moments about that point.

*velocity,*

velocity[m/s]= change in displacement[m]÷change in time[s]

Displacement is a distance in a specific direction.Therefore, velocity is a speed in a specific direction.

*acceleration,*

acceleration[m/s^{2}]= change in velocity[m/s][s]÷ change in time

Acceleration also has an associated direction.

An object is accelerating if the velocity changes, this can be through either the speed changing or the direction of travel changing.

*equations of motion (SUVAT),*

s - displacement[m]

u - initial velocity[m/s]

v - final velocity[m/s]

a - acceleration[m/s^{2}]

t - time[s]

The four SUVAT equations are only applicable to situations where the acceleration is constant.

*force,*

Force[N]= Mass[kg][m/s× Acceleration^{2}]

[kgm/s]= Change in momentum[s]÷ Change in time

This is Newton's famous 2nd law.

If there are multiple forces acting on an object, the mass times acceleration is equal to the sum of all the forces (also known as the resultant force).

If the forces are in equilibrium (the resultant force equals zero), the acceleration is constant. Hence, the object either stays at rest or moves in a straight line at constant speed.

*impulse,*

Impulse[kgm/s]= Force[N][s]× Change in time

[kgm/s]= Change in momentum

*work,*

Work done[J]= Force[N][m]× Distance travelled× Cosine of the angle between the force and the direction of travel

The cosine term is included to make sure the Force is multiplied by the distance travelled in the direction of the force.

Forces acting against the motion of an object do negative work.

*energy,*

Kinetic energy[J]= 1/2[kg]×Mass[m× Velocity squared^{2}/s^{2}]

Kinetic energy is energy stored by objects that are moving. It is equal to the work done to accelerate the object from rest up to their current speed.

Change in gravitational potential energy[J]= Mass[kg][m]× Gravitational acceleration× Change in height

Gravitational potential energy is stored in objects that have been raised against a gravitational field. This is equal to the work done in lifting them.

Mechanical energy is the sum of kinetic energy and potential energy, this is conserved if there are no frictional forces involved.

*power,*

Power[W]= Change in work done[J][s]÷ Change in time

[N]= Force[m/s]× Velocity

The second equation is only true if the force is in the same direction as the velocity.

The efficiency is always a value between 0 and 1, and commonly converted to a percentage between 0% and 100%.

## Materials

*density,*

Density[kg/m^{3}]= Mass[kg][mVolume÷^{3}]

*Hooke's law,*

Force needed to compress (or extend) a spring[N]= Spring constant[N/m][m]× Spring extension

Hooke's law describes how a spring behaves for small forces (larger forces will permanently deform the spring).

Spring extension can be positive or negative depending on whether its an extension or compression.

*tensile stress,*

Tensile stress[N/m^{2}]= Force applied to material[N][m÷ Area^{2}]

Tensile means that the material is under a tension, stretching the material.

*tensile strain,*

Tensile strain = Change in length[m][m]÷ Length

*Young's modulus,*

Young's modulus is a measure of the stiffness of a solid material.

*energy stored,*

Elastic energy[J]= 1/2[N]× Elastic force[m]× Change in length

Elastic energy is potential energy stored from work done to distort the shape of an elastic material (such as a spring).

## Electricity

*current,*

Current[A]= Change in electric charge[C]÷ Change in time[s]

Electricity is the flow of charge carriers, most commonly electrons. Current is the rate of flow of charge.

*potential difference,*

Voltage (also called potential difference)[V]= Work done[J]÷ Electric charge[C]

Voltage is the work done to move the charge carriers (per unit charge).

*resistance,*

Resistance[Ω]= Voltage[V]÷ Current[A]

Resistance is a measure of opposition to the flow of charge. For example, collisions of electrons with metal atoms slowing down their flow.

*resistivity,*

Resistivity[Ωm]= Resistance[Ω]× Cross-sectional area[m^{2}]÷ Length[m]

Resistivity is a property of a material that is a measure of how resistant it is to electric current.

There are three methods to increase the electrical resistance of an object: decrease the cross-sectional area, increase the length oruse a material with a higher resistivity.

*resistors in series,*

Total resistance= Sum of individual resistances

For resistors in series, the current through each resistor is the same but the voltages differ.

*resistors in parallel,*

Inverse of total resistance = Sum of the inverse of individual resistances

For resistors in parallel, the voltage is the same for each resistor but the current flowing through each is different.

*power,*

Power[W]= Current[A]× Voltage[V]

= Current squared[A^{2}]× Resistance[Ω]

= Voltage squared[V^{2}]÷ Resistance[Ω]

*emf,*

Electromotive force[V]= Energy provided[J]÷ Electrical charge[C]

= Current[A][Ω]× (Load Resistance[Ω]+ Internal resistance)

Emf is the energy per unit charge that a device, such as a battery, puts into a circuit.

Batteries aren't perfect and this is inefficiency is represented by an internal resistance.

The total resistance of a circuit is the sum of the internal resistance of the power supply and the resistance of the rest of the circuit (known as the load resistance).

**© 2017 Sam Brind**

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