A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Angular Motion and Uniform Angular Acceleration — mark scheme explained
The short answer
Understanding angular motion is crucial in engineering physics, particularly when dealing with rotating systems such as wheels, gears, and turbines. This section covers key concepts like angular displacement, angular speed, angular velocity, and angular acceleration, along with their mathematical representations and graphical methods.
The question
A wheel starts from rest and accelerates uniformly at a rate of 2 rad/s 2 . Calculate the angular velocity after 5 seconds.
[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 equations, substitution of values, and final answers. For explanation questions, marks are given for clarity, completeness, and accuracy of the response.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Determine
- Find or establish a particular value or quantity, often using given data and equations.
- Explain
- Provide a clear and detailed account of how something works or why it happens.
- Derive
- Show the steps involved in obtaining a formula or equation from first principles.
- Sketch
- Draw a graph or diagram to represent a relationship or situation.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 2-3 minutes per mark. For a 5-mark question, spend approximately 10-15 minutes to ensure you have enough time to check your work.
- Identify the given values: initial angular velocity (ω 0 ) = 0 rad/s, angular acceleration (α) = 2 rad/s 2 , time (t) = 5 s.0 marks
- Use the equation for uniform angular acceleration: ω = ω 0 + αt.1 mark
- Substitute the values into the equation: ω = 0 + 2 × 5.2 marks
- Calculate the result: ω = 10 rad/s.1 mark
Final answer: 10 rad/s
Work through every step correctly and you earn all 4 marks.
Another worked example
A rotating disk has an initial angular velocity of 3 rad/s and a constant angular acceleration of -1.5 rad/s 2 . Calculate the angular displacement after 4 seconds.
- Identify the given values: initial angular velocity (ω 0 ) = 3 rad/s, angular acceleration (α) = -1.5 rad/s 2 , time (t) = 4 s, and initial angular displacement (θ 0 ) = 0 rad.0 marks
- Use the equation for uniform angular acceleration: θ = θ 0 + ω 0 t + (1/2)αt 2 .2 marks
- Substitute the values into the equation: θ = 0 + 3 × 4 + (1/2) × (-1.5) × 4 2 .2 marks
- Calculate the result: θ = 12 - 12 = 0 rad.1 mark
Final answer: 0 rad
Work through every step correctly and you earn all 5 marks.
Common mistakes
Using degrees instead of radians for angular displacement and related quantities.
Why it happens: Students often forget that in physics, angles are typically measured in radians. Using degrees can lead to incorrect calculations and answers.
Fix: Always use radians when dealing with angular motion problems. Convert any given angles from degrees to radians if necessary.
Forgetting to use the right-hand rule to determine the direction of angular velocity and acceleration.
Why it happens: The right-hand rule is crucial for determining the direction of vector quantities like angular velocity and acceleration. Forgetting this can lead to incorrect signs in calculations.
Fix: Practice using the right-hand rule regularly. Point your right thumb along the axis of rotation, and the direction in which your fingers curl represents the positive direction of angular velocity and acceleration.
Misapplying the equations for uniform angular acceleration in non-uniform cases.
Why it happens: The equations for uniform angular acceleration are only valid when the angular acceleration is constant. Using them in situations where the angular acceleration changes can lead to incorrect results.
Fix: Always check if the problem states that the angular acceleration is constant before applying these equations. If it's not, use other methods or derive the necessary equations from first principles.
Confusing angular speed and angular velocity.
Why it happens: Angular speed is a scalar quantity (magnitude only), while angular velocity is a vector quantity (magnitude and direction). Confusing the two can lead to incorrect answers, especially in problems involving direction.
Fix: Always specify whether you are dealing with angular speed or angular velocity. Use the right-hand rule to determine the direction of angular velocity when necessary.
Failing to check units and dimensions in calculations.
Why it happens: Inconsistent units can lead to incorrect answers. For example, using seconds for time but radians per minute for angular speed will result in a dimensionally inconsistent equation.
Fix: Always ensure that all quantities have consistent units before performing calculations. Convert units as needed and double-check the dimensions of your final answer.
Not using the correct initial conditions when applying the equations for uniform angular acceleration.
Why it happens: The equations for uniform angular acceleration often require initial conditions (e.g., initial angular velocity and displacement). Forgetting to use these can lead to incorrect results.
Fix: Always identify and write down the initial conditions given in the problem. Use these values when applying the equations for uniform angular acceleration.
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 Angular Velocity | Find the final angular velocity of a wheel under uniform angular acceleration. | 4 |
| Calculate Angular Displacement | Use a rotational kinematics equation to find angular displacement after a given time. | 5 |
| Angular Acceleration Calculation | Use rotational kinematics to find angular acceleration from initial velocity and angular displacement. | 4 |
| Angular Displacement Calculation | Calculate the angular displacement of a wheel undergoing uniform angular acceleration from rest. | 5 |
| 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.