Source: https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-3-gravitational-potential

[Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [A Level](https://senecalearning.com/en-gb/revision-notes/a-level.md) › [Physics](https://senecalearning.com/en-gb/revision-notes/a-level/physics.md) › [AQA](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa.md) › Gravitational Potential

# Gravitational Potential

Physics: AQA A Level, topic 7.2.3

## Gravitational Potential

Understanding gravitational potential lets us consider the energy changes that objects moving in gravitational fields experience.

### Zero value

![Zero value](https://image-v2.cdn.app.senecalearning.com/2018-09/89c1e0f1-8dbd-4aa1-99a1-6c1144bd51e2/infinity-8-eight-.jpg)

- The zero value of gravitational potentials is defined as being at an infinite distance away from the mass generating the field.
- This is done so that when a small test mass is placed in the gravitational field, the test mass has work done on it by the original mass and gains kinetic energy (KE).
- To gain that KE, the object must have lost gravitational potential energy (GPE). In other words, the gravitational potential has become more negative.

### Example

![Example](https://image-v2.cdn.app.senecalearning.com/2018-09/bb20f207-9943-4cb4-97ce-256dce6f0c68/sheet-white-gravity-.jpg)

- Imagine a rubber sheet with a heavy object in the middle.
- The sheet is deformed downwards. The undeflected sheet is defined to be at zero potential.
- You can find the gravitational potential difference by subtracting the initial gravitational potential from the final gravitational potential.
 - E.g. In the diagram, the object has dropped from a potential of -30 J/kg to -50 J/kg. 
 - The change is -50 - (-30) = -20 J/kg. 
 - There has a been a drop in potential of 20 J/kg.

### Work done on a moving mass

![Work done on a moving mass](https://image-v2.cdn.app.senecalearning.com/2018-09/3816c6f1-aefa-4db8-b7fd-4f5306c50dcb/earth-planet-gravity-.jpg)

- The work done on a moving mass in that gravitational potential can be found by multiplying the change in potential by the mass.
- On the previous slide, if the mass of the object was 2.0 kg, then the work done on the mass would be 2.0 × 20 = 40 J.
- We could say that the 2.0 kg mass has lost 40 J of GPE, or that the large mass has done 40 J of work on the mass.

### Work done 2

![Work done 2](https://image-v2.cdn.app.senecalearning.com/2018-08/59da4c24-8aaf-4619-bf2f-6bb4190471f2/satellite.png)

- If an object moves along an equipotential surface, then the potential has not changed and no work has been done on the object.
- This is like satellites in circular orbit around a planet.
 - The planet does no work on the satellites. So there is no loss in potential, and no loss in GPE (the radius of the orbit does not change). This means the satellite does not change KE (and so has constant speed).

## Gravitational Potential Graphs

Gravitational potential graphs, gravitational field strengths and changes in gravitational potentials are all inter-linked.

### Gravitational potential

![Gravitational potential](https://image-v2.cdn.app.senecalearning.com/2018-08/77f7edce-ab31-4f9d-82d4-b4c634bb19fe/Gravitational%20Potential%20vs%20distance.png)

- The gravitational potential surrounding a planet or point mass is given by the formula $$V = -\frac{GM}{r}$$.
- The minus sign is important because it signifies an attractive force.

### Gravitational potential

![Gravitational potential](https://image-v2.cdn.app.senecalearning.com/2018-08/dd878f45-2f80-456c-b886-733cdb635239/Gravitational%20Potential%20vs%20distance.png)

- The graph shows the variation of gravitational potential with distance from a point mass.

### Gravitational field strength

![Gravitational field strength](https://image-v2.cdn.app.senecalearning.com/2018-08/9ab50a9d-298e-4f28-8e4b-0fa67e26c385/Gravitational%20field%20strength%20vs%20distance.png)

- The graph shows the variation of gravitational field strength with distance from a point mass.

### Gradient

![Gradient](https://image-v2.cdn.app.senecalearning.com/2018-09/fbc64f8c-1644-4cf4-9ed9-6d821bd8044d/grav-potential-distance-gradient.png)

- The -1 × (gradient of the gravitational potential) graph gives the variation of the gravitational field strength with distance.
- In a similar way, the gradient of a displacement-time graph gives the velocity-time graph.

### Area under graph

![Area under graph](https://image-v2.cdn.app.senecalearning.com/2018-09/c05fc71b-fd44-463a-b270-553fc6aacc04/grav-field-distance-integral.png)

- The reverse operation (i.e. finding the area between the curve and the distance axis) for a gravitational field strength against distance graph will give the change in potential.

## Test yourself on Gravitational Potential

- A satellite orbiting a planet has a gravitational potential energy of -1000 J.  It propels itself up so that it now has a gravitational potential energy of -600 J.  How much work has been done by the satellite?
- A satellite orbiting a planet has a gravitational potential energy of -60 J.  It propels itself up so that it now has a gravitational potential energy of -20 J.  How much work has been done by the satellite?
- What graph is formed when we take the negative of the gradient of a V-r (gravitational potential against distance) graph?
- What do we find if we take the area under a gravitational field vs distance graph?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/890da800-6a58-11e8-973c-cb81832c8407/section/92a6e8e8-54dc-4fa2-abe6-8dfbbd8a90b4/session)

- Previous topic: [7.2.2 Gravitational Field Strength](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-2-gravitational-field-strength.md)
- Next topic: [7.2.4 Orbits of Planets & Satellites](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-4-orbits-of-planets-and-satellites.md)

## Physics: AQA A Level contents

### 1 Measurements & Errors
- 1.1 Measurements & Errors
  - [1.1.1 SI Base Units](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-1-si-base-units.md)
  - [1.1.2 Combining SI Units](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-2-combining-si-units.md)
  - [1.1.3 Prefixes of Units](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-3-prefixes-of-units.md)
  - [1.1.4 Standard Form](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-4-standard-form.md)
  - [1.1.5 Converting Units](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-5-converting-units.md)
  - [1.1.6 End of Topic Test - Units & Prefixes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-6-end-of-topic-test-units-and-prefixes.md)
  - [1.1.7 Limitation of Physical Measurements](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-7-limitation-of-physical-measurements.md)
  - [1.1.8 Uncertainty](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-8-uncertainty.md)
  - [1.1.9 Estimation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-9-estimation.md)
  - [1.1.10 End of Topic Test - Measurements & Errors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-10-end-of-topic-test-measurements-and-errors.md)
  - [1.1.11 Diagnostic Misconceptions - Converting between SI](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-11-diagnostic-misconceptions-converting-between-si.md)
  - [1.1.12 Diagnostic Misconceptions - SI & Area/Volume](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/1-1-12-diagnostic-misconceptions-si-and-areavolume.md)

### 2 Particles & Radiation
- 2.1 Particles
  - [2.1.1 Atomic Model](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-1-atomic-model.md)
  - [2.1.2 Specific Charge, Protons & Neutron Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-2-specific-charge-protons-and-neutron-numbers.md)
  - [2.1.3 End of Topic Test - Atomic Model](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-3-end-of-topic-test-atomic-model.md)
  - [2.1.4 Isotopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-4-isotopes.md)
  - [2.1.5 Stable & Unstable Nuclei](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-5-stable-and-unstable-nuclei.md)
  - [2.1.6 End of Topic Test - Isotopes & Nuclei](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-6-end-of-topic-test-isotopes-and-nuclei.md)
  - [2.1.7 A-A* (AO3/4) - Stable & Unstable Nuclei](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-7-a-a-ao34-stable-and-unstable-nuclei.md)
  - [2.1.8 Particles, Antiparticles & Photons](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-8-particles-antiparticles-and-photons.md)
  - [2.1.9 Particle Interactions](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-9-particle-interactions.md)
  - [2.1.10 Classification of Particles](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-10-classification-of-particles.md)
  - [2.1.11 End of Topic Test - Particles & Interactions](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-11-end-of-topic-test-particles-and-interactions.md)
  - [2.1.12 Quarks & Antiquarks](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-12-quarks-and-antiquarks.md)
  - [2.1.13 Application of Conservation Laws](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-13-application-of-conservation-laws.md)
  - [2.1.14 End of Topic Test - Leptons & Quarks](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-14-end-of-topic-test-leptons-and-quarks.md)
  - [2.1.15 Exam-Style Question -  Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-1-15-exam-style-question-radioactive-decay.md)
- 2.2 Electromagnetic Radiation & Quantum Phenomena
  - [2.2.1 The Photoelectric Effect](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-1-the-photoelectric-effect.md)
  - [2.2.2 The Photoelectric Effect Explanation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-2-the-photoelectric-effect-explanation.md)
  - [2.2.3 End of Topic Test - The Photoelectric Effect](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-3-end-of-topic-test-the-photoelectric-effect.md)
  - [2.2.4 Collisions of Electrons with Atoms](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-4-collisions-of-electrons-with-atoms.md)
  - [2.2.5 Energy Levels & Photon Emission](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-5-energy-levels-and-photon-emission.md)
  - [2.2.6 Wave-Particle Duality](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-6-wave-particle-duality.md)
  - [2.2.7 End of Topic Test - Absorption & Emission](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-7-end-of-topic-test-absorption-and-emission.md)
  - [2.2.8 Diagnostic Misconceptions - Electron Volts](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-8-diagnostic-misconceptions-electron-volts.md)
  - [2.2.9 Diagnostic Misconceptions - Converting eV & Joules](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/2-2-9-diagnostic-misconceptions-converting-ev-and-joules.md)

### 3 Waves
- 3.1 Progressive & Stationary Waves
  - [3.1.1 Progressive Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-1-progressive-waves.md)
  - [3.1.2 Wave Speed & Phase Difference](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-2-wave-speed-and-phase-difference.md)
  - [3.1.3 Longitudinal & Transverse Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-3-longitudinal-and-transverse-waves.md)
  - [3.1.4 End of Topic Test - Progressive Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-4-end-of-topic-test-progressive-waves.md)
  - [3.1.5 Polarisation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-5-polarisation.md)
  - [3.1.6 Stationary Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-6-stationary-waves.md)
  - [3.1.7 Stationary Waves 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-7-stationary-waves-2.md)
  - [3.1.8 End of Topic Test - Polarisation & Stationary Wave](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-8-end-of-topic-test-polarisation-and-stationary-wave.md)
  - [3.1.9 A-A* (AO3/4) - Stationary Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-1-9-a-a-ao34-stationary-waves.md)
- 3.2 Refraction, Diffraction & Interference
  - [3.2.1 Interference](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-1-interference.md)
  - [3.2.2 Interference 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-2-interference-2.md)
  - [3.2.3 End of Topic Test - Interference](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-3-end-of-topic-test-interference.md)
  - [3.2.4 Diffraction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-4-diffraction.md)
  - [3.2.5 Diffraction Gratings](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-5-diffraction-gratings.md)
  - [3.2.6 End of Topic Test - Diffraction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-6-end-of-topic-test-diffraction.md)
  - [3.2.7 Refraction at a Plane Surface](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-7-refraction-at-a-plane-surface.md)
  - [3.2.8 Internal Reflection & Fibre Optics](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-8-internal-reflection-and-fibre-optics.md)
  - [3.2.9 End of Topic Test - Refraction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-9-end-of-topic-test-refraction.md)
  - [3.2.10 Exam-Style Question - Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/3-2-10-exam-style-question-waves.md)

### 4 Mechanics & Materials
- 4.1 Force, Energy & Momentum
  - [4.1.1 Scalars & Vectors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-1-scalars-and-vectors.md)
  - [4.1.2 Vector Problems](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-2-vector-problems.md)
  - [4.1.3 End of Topic Test - Scalars & Vectors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-3-end-of-topic-test-scalars-and-vectors.md)
  - [4.1.4 Moments](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-4-moments.md)
  - [4.1.5 Centre of Mass](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-5-centre-of-mass.md)
  - [4.1.6 End of Topic Test - Moments & Centre of Mass](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-6-end-of-topic-test-moments-and-centre-of-mass.md)
  - [4.1.7 Motion in a Straight Line](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-7-motion-in-a-straight-line.md)
  - [4.1.8 Graphs of Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-8-graphs-of-motion.md)
  - [4.1.9 Bouncing Ball Example](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-9-bouncing-ball-example.md)
  - [4.1.10 End of Topic Test - Motion in a Straight Line](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-10-end-of-topic-test-motion-in-a-straight-line.md)
  - [4.1.11 Acceleration Due to Gravity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-11-acceleration-due-to-gravity.md)
  - [4.1.12 Projectile Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-12-projectile-motion.md)
  - [4.1.13 Friction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-13-friction.md)
  - [4.1.14 Terminal Speed](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-14-terminal-speed.md)
  - [4.1.15 End of Topic Test - Acceleration Due to Gravity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-15-end-of-topic-test-acceleration-due-to-gravity.md)
  - [4.1.16 Newton's Laws](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-16-newtons-laws.md)
  - [4.1.17 Momentum](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-17-momentum.md)
  - [4.1.18 Momentum 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-18-momentum-2.md)
  - [4.1.19 End of Topic Test - Newton's Laws & Momentum](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-19-end-of-topic-test-newtons-laws-and-momentum.md)
  - [4.1.20 A-A* (AO3/4) - Newton's Third Law](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-20-a-a-ao34-newtons-third-law.md)
  - [4.1.21 Work & Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-21-work-and-energy.md)
  - [4.1.22 Power & Efficiency](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-22-power-and-efficiency.md)
  - [4.1.23 Conservation of Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-23-conservation-of-energy.md)
  - [4.1.24 End of Topic Test - Work, Energy & Power](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-24-end-of-topic-test-work-energy-and-power.md)
  - [4.1.25 Exam-Style Question - Forces](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-25-exam-style-question-forces.md)
  - [4.1.26 Diagnostic Misconceptions - Perpendicular Vectors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-26-diagnostic-misconceptions-perpendicular-vectors.md)
  - [4.1.27 Diagnostic Misconceptions - Weight Acts Downwards](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-27-diagnostic-misconceptions-weight-acts-downwards.md)
  - [4.1.28 Diagnostic Misconceptions - Acceleration Direction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-28-diagnostic-misconceptions-acceleration-direction.md)
  - [4.1.29 Diagnostic Misconceptions - Stationary Objects](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-29-diagnostic-misconceptions-stationary-objects.md)
  - [4.1.30 Diagnostic Misconceptions - Action & Reaction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-30-diagnostic-misconceptions-action-and-reaction.md)
  - [4.1.31 Diagnostic Misconceptions - RF Direction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-31-diagnostic-misconceptions-rf-direction.md)
  - [4.1.32 Diagnostic Misconceptions - RF Acceleration](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-32-diagnostic-misconceptions-rf-acceleration.md)
  - [4.1.33 Diagnostic Misconceptions - Change in Momentum](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-1-33-diagnostic-misconceptions-change-in-momentum.md)
- 4.2 Materials
  - [4.2.1 Density](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-2-1-density.md)
  - [4.2.2 Bulk Properties of Solids](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-2-2-bulk-properties-of-solids.md)
  - [4.2.3 Energy in Materials](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-2-3-energy-in-materials.md)
  - [4.2.4 Young Modulus](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-2-4-young-modulus.md)
  - [4.2.5 End of Topic Test - Materials](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/4-2-5-end-of-topic-test-materials.md)

### 5 Electricity
- 5.1 Current Electricity
  - [5.1.1 Basics of Electricity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-1-basics-of-electricity.md)
  - [5.1.2 Current-Voltage Characteristics](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-2-current-voltage-characteristics.md)
  - [5.1.3 End of Topic Test - Basics of Electricity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-3-end-of-topic-test-basics-of-electricity.md)
  - [5.1.4 Resistivity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-4-resistivity.md)
  - [5.1.5 Superconductivity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-5-superconductivity.md)
  - [5.1.6 A-A* (AO3/4) - Superconductivity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-6-a-a-ao34-superconductivity.md)
  - [5.1.7 End of Topic Test - Resistivity & Superconductors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-7-end-of-topic-test-resistivity-and-superconductors.md)
  - [5.1.8 Circuits](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-8-circuits.md)
  - [5.1.9 Power and Conservation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-9-power-and-conservation.md)
  - [5.1.10 Potential Divider](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-10-potential-divider.md)
  - [5.1.11 Emf & Internal Resistance](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-11-emf-and-internal-resistance.md)
  - [5.1.12 End of Topic Test - Power & Potential](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-12-end-of-topic-test-power-and-potential.md)
  - [5.1.13 Exam-Style Question - Resistance](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-13-exam-style-question-resistance.md)
  - [5.1.14 Diagnostic Misconceptions - Constant Current](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-14-diagnostic-misconceptions-constant-current.md)
  - [5.1.15 Diagnostic Misconceptions - Potential Difference](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/5-1-15-diagnostic-misconceptions-potential-difference.md)

### 6 Further Mechanics & Thermal Physics (A2 only)
- 6.1 Periodic Motion (A2 only)
  - [6.1.1 Circular Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-1-circular-motion.md)
  - [6.1.2 Circular Motion 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-2-circular-motion-2.md)
  - [6.1.3 End of Topic Test - Circular Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-3-end-of-topic-test-circular-motion.md)
  - [6.1.4 Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-4-simple-harmonic-motion.md)
  - [6.1.5 Simple Harmonic Systems](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-5-simple-harmonic-systems.md)
  - [6.1.6 Energy in Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-6-energy-in-simple-harmonic-motion.md)
  - [6.1.7 Resonance](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-7-resonance.md)
  - [6.1.8 End of Topic Test - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-8-end-of-topic-test-simple-harmonic-motion.md)
  - [6.1.9 A-A* (AO3/4) - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-1-9-a-a-ao34-simple-harmonic-motion.md)
- 6.2 Thermal Physics (A2 only)
  - [6.2.1 Thermal Energy Transfer](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-1-thermal-energy-transfer.md)
  - [6.2.2 Thermal Energy Transfer Experiments](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-2-thermal-energy-transfer-experiments.md)
  - [6.2.3 Ideal Gases](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-3-ideal-gases.md)
  - [6.2.4 Ideal Gases 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-4-ideal-gases-2.md)
  - [6.2.5 Boyle's Law & Charles' Law](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-5-boyles-law-and-charles-law.md)
  - [6.2.6 Molecular Kinetic Theory Model](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-6-molecular-kinetic-theory-model.md)
  - [6.2.7 Molecular Kinetic Theory Model 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-7-molecular-kinetic-theory-model-2.md)
  - [6.2.8 End of Topic Test - Thermal Energy & Ideal Gases](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-8-end-of-topic-test-thermal-energy-and-ideal-gases.md)
  - [6.2.9 Exam-Style Question - Ideal Gases](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-9-exam-style-question-ideal-gases.md)
  - [6.2.10 Diagnostic Misconceptions - Material & Mass](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-10-diagnostic-misconceptions-material-and-mass.md)
  - [6.2.11 Diagnostic Misconceptions - No Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/6-2-11-diagnostic-misconceptions-no-energy.md)

### 7 Fields & Their Consequences (A2 only)
- 7.1 Fields (A2 only)
  - [7.1.1 Fields](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-1-1-fields.md)
- 7.2 Gravitational Fields (A2 only)
  - [7.2.1 Newton's Law](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-1-newtons-law.md)
  - [7.2.2 Gravitational Field Strength](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-2-gravitational-field-strength.md)
  - [7.2.3 Gravitational Potential](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-3-gravitational-potential.md)
  - [7.2.4 Orbits of Planets & Satellites](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-4-orbits-of-planets-and-satellites.md)
  - [7.2.5 Escape Velocity & Synchronous Orbits](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-5-escape-velocity-and-synchronous-orbits.md)
  - [7.2.6 End of Topic Test - Gravitational Fields](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-2-6-end-of-topic-test-gravitational-fields.md)
- 7.3 Electric Fields (A2 only)
  - [7.3.1 Coulomb's Law](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-1-coulombs-law.md)
  - [7.3.2 Electric Field Strength](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-2-electric-field-strength.md)
  - [7.3.3 Electric Field Strength 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-3-electric-field-strength-2.md)
  - [7.3.4 Electric Potential](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-4-electric-potential.md)
  - [7.3.5 End of Topic Test - Electric Fields](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-5-end-of-topic-test-electric-fields.md)
  - [7.3.6 A-A* (AO3/4) - Electric and Gravitational Field](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-3-6-a-a-ao34-electric-and-gravitational-field.md)
- 7.4 Capacitance (A2 only)
  - [7.4.1 Capacitance](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-4-1-capacitance.md)
  - [7.4.2 Parallel Plate Capacitor](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-4-2-parallel-plate-capacitor.md)
  - [7.4.3 Energy Stored by a Capacitor](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-4-3-energy-stored-by-a-capacitor.md)
  - [7.4.4 Capacitor Discharge](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-4-4-capacitor-discharge.md)
  - [7.4.5 Capacitor Charge](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-4-5-capacitor-charge.md)
- 7.5 Magnetic Fields (A2 only)
  - [7.5.1 Magnetic Flux Density](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-1-magnetic-flux-density.md)
  - [7.5.2 End of Topic Test - Capacitance & Flux Density](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-2-end-of-topic-test-capacitance-and-flux-density.md)
  - [7.5.3 Moving Charges in a Magnetic Field](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-3-moving-charges-in-a-magnetic-field.md)
  - [7.5.4 Magnetic Flux & Flux Linkage](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-4-magnetic-flux-and-flux-linkage.md)
  - [7.5.5 Electromagnetic Induction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-5-electromagnetic-induction.md)
  - [7.5.6 Electromagnetic Induction 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-6-electromagnetic-induction-2.md)
  - [7.5.7 Alternating Currents](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-7-alternating-currents.md)
  - [7.5.8 Operation of a Transformer](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-8-operation-of-a-transformer.md)
  - [7.5.9 Magnetic Flux Density](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-9-magnetic-flux-density.md)
  - [7.5.10 End of Topic Test - Electromagnetic Induction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/7-5-10-end-of-topic-test-electromagnetic-induction.md)

### 8 Nuclear Physics (A2 only)
- 8.1 Radioactivity (A2 only)
  - [8.1.1 Rutherford Scattering](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-1-rutherford-scattering.md)
  - [8.1.2 Alpha & Beta Radiation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-2-alpha-and-beta-radiation.md)
  - [8.1.3 Gamma Radiation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-3-gamma-radiation.md)
  - [8.1.4 Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-4-radioactive-decay.md)
  - [8.1.5 Half Life](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-5-half-life.md)
  - [8.1.6 End of Topic Test - Radioactivity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-6-end-of-topic-test-radioactivity.md)
  - [8.1.7 Nuclear Instability](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-7-nuclear-instability.md)
  - [8.1.8 Nuclear Radius](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-8-nuclear-radius.md)
  - [8.1.9 Mass & Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-9-mass-and-energy.md)
  - [8.1.10 Binding Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-10-binding-energy.md)
  - [8.1.11 Induced Fission](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-11-induced-fission.md)
  - [8.1.12 Safety Aspects of Nuclear Reactors](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-12-safety-aspects-of-nuclear-reactors.md)
  - [8.1.13 End of Topic Test - Nuclear Physics](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-13-end-of-topic-test-nuclear-physics.md)
  - [8.1.14 A-A* (AO3/4) - Nuclear Fusion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/8-1-14-a-a-ao34-nuclear-fusion.md)

### 9 Option: Astrophysics (A2 only)
- 9.1 Telescopes (A2 only)
  - [9.1.1 Astronomical Telescopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-1-1-astronomical-telescopes.md)
  - [9.1.2 Reflecting Telescopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-1-2-reflecting-telescopes.md)
  - [9.1.3 Single Dish Radio Telescopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-1-3-single-dish-radio-telescopes.md)
  - [9.1.4 Large Diameter Telescopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-1-4-large-diameter-telescopes.md)
- 9.2 Classification of Stars (A2 only)
  - [9.2.1 Classification by Luminosity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-1-classification-by-luminosity.md)
  - [9.2.2 Absolute Magnitude](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-2-absolute-magnitude.md)
  - [9.2.3 Black Body Radiation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-3-black-body-radiation.md)
  - [9.2.4 Stellar Spectral Classes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-4-stellar-spectral-classes.md)
  - [9.2.5 Hertzsprung-Russell Diagrams](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-5-hertzsprung-russell-diagrams.md)
  - [9.2.6 Astronomical Objects](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-2-6-astronomical-objects.md)
- 9.3 Cosmology (A2 only)
  - [9.3.1 Doppler Effect](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-3-1-doppler-effect.md)
  - [9.3.2 Hubble's Law](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-3-2-hubbles-law.md)
  - [9.3.3 Quasars](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-3-3-quasars.md)
  - [9.3.4 Detecting Exoplanets](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/9-3-4-detecting-exoplanets.md)

### 10 Option: Medical Physics (A2 only)
- 10.1 Physics of the Eye (A2 only)
  - [10.1.1 Physics of Vision](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-1-1-physics-of-vision.md)
  - [10.1.2 Defects of Vision](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-1-2-defects-of-vision.md)
  - [10.1.3 Lenses](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-1-3-lenses.md)
  - [10.1.4 Correcting Defects of Vision](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-1-4-correcting-defects-of-vision.md)
- 10.2 Physics of the Ear (A2 only)
  - [10.2.1 Structure of the Ear](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-2-1-structure-of-the-ear.md)
  - [10.2.2 Sensitivity of the Ear](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-2-2-sensitivity-of-the-ear.md)
  - [10.2.3 Hearing Defects](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-2-3-hearing-defects.md)
- 10.3 Biological Measurement (A2 only)
  - [10.3.1 Electrocardiography (ECG)](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-3-1-electrocardiography-ecg.md)
- 10.4 Non-Ionising Imaging (A2 only)
  - [10.4.1 Ultrasound Imaging](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-4-1-ultrasound-imaging.md)
  - [10.4.2 Ultrasound Imaging 2](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-4-2-ultrasound-imaging-2.md)
  - [10.4.3 Fibre Optics & Endoscopy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-4-3-fibre-optics-and-endoscopy.md)
  - [10.4.4 Magnetic Resonance Scanning](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-4-4-magnetic-resonance-scanning.md)
- 10.5 X-Ray Imaging (A2 only)
  - [10.5.1 Diagnostic X-Rays](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-5-1-diagnostic-x-rays.md)
  - [10.5.2 X-Ray Image Processing](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-5-2-x-ray-image-processing.md)
  - [10.5.3 Absorption of X-Rays](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-5-3-absorption-of-x-rays.md)
  - [10.5.4 CT Scanners](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-5-4-ct-scanners.md)
- 10.6 Radionuclide Imaging & Therapy (A2 only)
  - [10.6.1 Imaging Techniques](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-1-imaging-techniques.md)
  - [10.6.2 Half Life](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-2-half-life.md)
  - [10.6.3 Gamma Camera](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-3-gamma-camera.md)
  - [10.6.4 High Energy X-Rays](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-4-high-energy-x-rays.md)
  - [10.6.5 Radioactive Implants](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-5-radioactive-implants.md)
  - [10.6.6 Imaging Comparisons](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/10-6-6-imaging-comparisons.md)

### 11 Option: Engineering Physics (A2 only)
- 11.1 Rotational Dynamics (A2 only)
  - [11.1.1 Moment of Inertia](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-1-moment-of-inertia.md)
  - [11.1.2 Rotational Kinetic Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-2-rotational-kinetic-energy.md)
  - [11.1.3 Rotational Motion](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-3-rotational-motion.md)
  - [11.1.4 Torque & Angular Acceleration](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-4-torque-and-angular-acceleration.md)
  - [11.1.5 Angular Momentum](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-5-angular-momentum.md)
  - [11.1.6 Angular Work & Power](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-1-6-angular-work-and-power.md)
- 11.2 Thermodynamics & Engines (A2 only)
  - [11.2.1 First Law of Thermodynamics](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-1-first-law-of-thermodynamics.md)
  - [11.2.2 Non-Flow Processes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-2-non-flow-processes.md)
  - [11.2.3 p-V Diagrams](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-3-p-v-diagrams.md)
  - [11.2.4 Engine Cycles](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-4-engine-cycles.md)
  - [11.2.5 Second Law & Engines](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-5-second-law-and-engines.md)
  - [11.2.6 Reversed Heat Engines](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/11-2-6-reversed-heat-engines.md)

### 12 Option: Turning Points in Physics (A2 only)
- 12.1 Discovery of the Electron (A2 only)
  - [12.1.1 Cathode Rays](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-1-1-cathode-rays.md)
  - [12.1.2 Thermionic Electron Emission](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-1-2-thermionic-electron-emission.md)
  - [12.1.3 Electron Specific Charge](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-1-3-electron-specific-charge.md)
  - [12.1.4 Millikan's Experiment](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-1-4-millikans-experiment.md)
- 12.2 Wave-Particle Duality (A2 only)
  - [12.2.1 Newton's & Huygen's Theories of Light](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-2-1-newtons-and-huygens-theories-of-light.md)
  - [12.2.2 Electromagnetic Waves](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-2-2-electromagnetic-waves.md)
  - [12.2.3 Photoelectricity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-2-3-photoelectricity.md)
  - [12.2.4 Wave-Particle Duality](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-2-4-wave-particle-duality.md)
  - [12.2.5 Electron Microscopes](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-2-5-electron-microscopes.md)
- 12.3 Special Relativity (A2 only)
  - [12.3.1 Michelson-Morley Experiment](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-3-1-michelson-morley-experiment.md)
  - [12.3.2 Einstein's Theory of Special Relativity](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-3-2-einsteins-theory-of-special-relativity.md)
  - [12.3.3 Time Dilation](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-3-3-time-dilation.md)
  - [12.3.4 Length Contraction](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-3-4-length-contraction.md)
  - [12.3.5 Mass & Energy](https://senecalearning.com/en-gb/revision-notes/a-level/physics/aqa/12-3-5-mass-and-energy.md)