A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Torque and Power in Rotating Machinery — mark scheme explained
The short answer
In the context of engineering physics, understanding the relationship between torque (T), power (P), work (W), angular displacement (θ), and angular velocity (ω) is crucial for analyzing rotating machinery. This spec point focuses on these relationships and the importance of accounting for frictional torque in such systems.
The question
A rotating machine has a torque of 50 N·m and an angular velocity of 10 rad/s. Calculate the power output of the machine.
[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 identifying correct values, using appropriate formulas, and performing accurate calculations. For conceptual questions, marks are given for clear and concise explanations that demonstrate understanding.
What the command words demand
- Calculate
- Perform a numerical calculation using given data and appropriate formulas.
- Explain
- Provide a clear and concise explanation of a concept or phenomenon.
- Determine
- Find the value of a quantity by applying relevant principles or formulas.
- Analyze
- Examine in detail the elements or structure of something, typically to identify patterns or relationships.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 2-3 minutes per mark for this topic to ensure you have enough time to carefully read the question, perform necessary calculations, and check your work.
- Identify the given values: T = 50 N·m, ω = 10 rad/s.0 marks
- Use the formula for power in rotational systems: P = T × ω.1 mark
- Substitute the given values into the formula: P = 50 N·m × 10 rad/s.1 mark
- Calculate the result: P = 500 W.2 marks
Final answer: 500 W
Work through every step correctly and you earn all 4 marks.
Another worked example
A flywheel with a radius of 0.5 m is subjected to a force of 20 N at its edge. Calculate the torque produced.
- Identify the given values: F = 20 N, r = 0.5 m.0 marks
- Use the formula for torque: T = F × r.1 mark
- Substitute the given values into the formula: T = 20 N × 0.5 m.1 mark
- Calculate the result: T = 10 N·m.1 mark
Final answer: 10 N·m
Work through every step correctly and you earn all 3 marks.
Common mistakes
Forgetting to convert revolutions to radians when calculating angular velocity.
Why it happens: Students often forget that angular displacement must be in radians for the formula ω = θ / t to work correctly.
Fix: Always convert revolutions to radians before using them in calculations. 1 revolution = 2π radians.
Using inconsistent units when performing calculations involving torque and power.
Why it happens: Students may mix different units, such as using newtons for force and meters for radius but forgetting to use seconds for time in angular velocity.
Fix: Ensure all units are consistent. For example, use SI units (newtons, meters, seconds) throughout the calculation.
Overlooking frictional torque when analyzing rotating machinery.
Why it happens: Students might focus only on the applied torque and ignore the opposing frictional torque, leading to incorrect efficiency calculations.
Fix: Always consider the impact of frictional torque in real-world applications. Account for it in your calculations to get a more accurate picture of system performance.
Confusing angular displacement (θ) with angular velocity (ω).
Why it happens: Students may mix up these two concepts, leading to errors in formulas and calculations.
Fix: Understand that angular displacement is the angle through which an object has turned, while angular velocity is the rate of change of this angle. Use θ for displacement and ω for velocity.
Incorrectly applying the formula for work in rotational systems.
Why it happens: Students might use the wrong formula or substitute values incorrectly, leading to incorrect results.
Fix: Always use the correct formula W = T × θ and ensure that torque (T) and angular displacement (θ) are correctly identified and substituted.
Failing to check the units of the final answer.
Why it happens: Students might perform calculations correctly but forget to verify that the final answer is in the correct unit (e.g., watts for power, joules for work).
Fix: Always double-check the units of your final answer to ensure they match the expected unit for the quantity being calculated.
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 Power | Find the power output using the torque and angular velocity of a rotating machine. | 4 |
| Calculate Torque | Find the torque from a force applied at the edge of a flywheel. | 3 |
| Calculate Angular Velocity | Find angular velocity from a number of revolutions completed in a given time. | 4 |
| Calculate Rotational Work | Use the torque and angular displacement to work out the work done. | 3 |
| Calculate Torque | Rearrange the power-torque equation and calculate torque from given power and angular velocity. | 4 |
| Total across these question types | 18 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.