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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
1. Identify the given values: I = 3 kg·m 2 , ω = 8 rad/s
- S2
2. Use the formula for energy stored in a flywheel: E = ½ I ω 2
- S3
3. Substitute the values into the formula: E = ½ × 3 kg·m 2 × (8 rad/s) 2
- S4
4. Calculate the energy: E = ½ × 3 × 64
- S5
5. Simplify to find the final answer: E = 96 J
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
1. Identify the given values: I = 3 kg·m 2 , ω = 8 rad/s
- S2
2. Use the formula for energy stored in a flywheel: E = ½ I ω 2
- S3
3. Substitute the values into the formula: E = ½ × 3 kg·m 2 × (8 rad/s) 2
- S4
4. Calculate the energy: E = ½ × 3 × 64
- S5
5. Simplify to find the final answer: E = 96 J
Final answer: 96 J
Common mistakes
- Confusing moment of inertia with mass. — 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. — 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. — Remind students to always square the angular velocity when using the formula E = ½ I ω 2 .
- Not converting units correctly. — 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. — 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. — Emphasize that the correct formula is E = ½ I ω 2 , and always include the 1/2 in calculations.
Where the marks go
- Full worked solution (all marking points)5 marks