A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Energy Storage in Flywheels and Their Applications — mark scheme explained
The short answer
Flywheels are mechanical devices that store rotational kinetic energy. They have a wide range of applications, from smoothing torque and speed in machines to storing energy in vehicles and production processes.
The question
A flywheel has a moment of inertia of 3 kg·m 2 and is rotating at an angular velocity of 8 rad/s. Calculate the energy stored in the flywheel.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, marks are typically awarded for correct use of formulas, substitution of values, and final answers. For explanation and description questions, marks are given for clarity, accuracy, and completeness of the response.
What the command words demand
- Calculate
- Perform a numerical calculation using given data and appropriate formulas.
- Explain
- Provide a clear and detailed account of how or why something happens, including relevant principles and concepts.
- Describe
- Give a detailed account of the characteristics, features, or processes involved.
- Compare
- Identify and explain similarities and differences between two or more items or concepts.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 2-3 minutes per mark to ensure you have enough time to read the question carefully, perform calculations accurately, and provide well-structured explanations.
- 1. Identify the given values: I = 3 kg·m 2 , ω = 8 rad/s0 marks
- 2. Use the formula for energy stored in a flywheel: E = ½ I ω 21 mark
- 3. Substitute the values into the formula: E = ½ × 3 kg·m 2 × (8 rad/s) 22 marks
- 4. Calculate the energy: E = ½ × 3 × 641 mark
- 5. Simplify to find the final answer: E = 96 J1 mark
Final answer: 96 J
Work through every step correctly and you earn all 5 marks.
Another worked example
A flywheel with a moment of inertia of 2 kg·m 2 is initially rotating at an angular velocity of 10 rad/s. It slows down to 5 rad/s due to friction. Calculate the energy lost by the flywheel.
- 1. Identify the initial and final angular velocities: ω initial = 10 rad/s , ω final = 5 rad/s0 marks
- 2. Use the formula for energy stored in a flywheel: E = ½ I ω 21 mark
- 3. Calculate the initial energy: E initial = ½ × 2 kg·m 2 × (10 rad/s) 21 mark
- 4. Simplify to find the initial energy: E initial = ½ × 2 × 100 = 100 J1 mark
- 5. Calculate the final energy: E final = ½ × 2 kg·m 2 × (5 rad/s) 21 mark
- 6. Simplify to find the final energy: E final = ½ × 2 × 25 = 25 J1 mark
- 7. Calculate the energy lost: E lost = E initial - E final0 marks
- 8. Simplify to find the final answer: E lost = 100 J - 25 J = 75 J1 mark
Final answer: 75 J
Work through every step correctly and you earn all 6 marks.
Common mistakes
Confusing moment of inertia with mass.
Why it happens: Students often mistake the moment of inertia for just the mass, forgetting that it also depends on the distribution of mass around the axis of rotation.
Fix: Emphasize that the moment of inertia is a measure of an object's resistance to changes in its rotational motion and depends on both mass and its distribution.
Using linear velocity instead of angular velocity.
Why it happens: Students sometimes use the formula for kinetic energy involving linear velocity (1/2 mv 2 ) instead of the correct formula for rotational kinetic energy (1/2 I ω 2 ).
Fix: Clarify that for flywheels, the relevant formula is E = ½ I ω 2 , where ω is the angular velocity.
Forgetting to square the angular velocity in calculations.
Why it happens: Students might forget that the energy stored in a flywheel is proportional to the square of the angular velocity, leading to incorrect calculations.
Fix: Remind students to always square the angular velocity when using the formula E = ½ I ω 2 .
Not converting units correctly.
Why it happens: Students may use inconsistent units, such as mixing kilograms and grams or meters and centimeters, leading to incorrect results.
Fix: Ensure that all units are consistent before performing calculations. For example, convert all masses to kilograms and lengths to meters.
Misinterpreting the role of flywheels in energy storage.
Why it happens: Students might not fully understand how flywheels store and release energy, leading to confusion about their applications.
Fix: Explain that flywheels store rotational kinetic energy and can release it when needed, making them useful for smoothing torque and speed fluctuations and storing energy in vehicles and production processes.
Forgetting to halve the moment of inertia in the formula.
Why it happens: Students might forget that the factor 1/2 is part of the formula for rotational kinetic energy, leading to incorrect calculations.
Fix: Emphasize that the correct formula is E = ½ I ω 2 , and always include the 1/2 in calculations.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Rotational Energy | Use the rotational kinetic energy formula to find the energy stored in a rotating flywheel. | 5 |
| Calculate Energy Loss | Find the rotational kinetic energy lost by a flywheel as it slows down. | 6 |
| Rotational Kinetic Energy | Find the new angular velocity of a flywheel after its stored rotational energy is doubled. | 6 |
| Rotational Kinetic Energy | Find the new angular velocity of a flywheel after its rotational kinetic energy is halved. | 6 |
| Total across these question types | 23 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.