AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Torque and angular acceleration (A-level only): T = Fr T = Iα
Torque (moment of a force) measures the turning effect of a force about an axis: T = Fr, where F is the force and r is the perpendicular distance from the axis to the line of action.
Checked against the AQA 7408 specification (opens in a new tab) on .
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Torque (moment of a force) measures the turning effect of a force about an axis: T = Fr, where F is the force and r is the perpendicular distance from the axis to the line of action. For a rotating rigid body, the resultant torque produces angular acceleration according to T = Iα, where I is the moment of inertia and α is angular acceleration in rad s⁻². These equations are the rotational analogues of F = ma and the moment equation. To solve problems, identify the axis, find the perpendicular distance, calculate resultant torque, then use T = Iα to find α, or combine with rotational kinematics.
What earns the marks
- Torque is defined by T = Fr, where r is the perpendicular distance from the axis to the line of action of the force, not necessarily the length of the object.
- The rotational form of Newton's second law is T = Iα, where I is the moment of inertia about the chosen axis and α is angular acceleration in rad s⁻².
- For several forces, calculate the resultant torque by taking clockwise and anticlockwise contributions with opposite signs before applying T = Iα.
- Moment of inertia depends on mass and its distribution about the axis, so the same torque produces different angular accelerations for different bodies or axes.
- Angular acceleration links to linear acceleration at a point by a = rα, allowing rotational and linear dynamics to be combined.
- The equations apply to a rigid body rotating about a fixed axis, with torque and moment of inertia taken about that same axis.
Common mistakes and how to put them right
Using the full length of a rod as r when the force is not perpendicular to it.
Put it right: Use the perpendicular distance from the axis to the line of action, or resolve the force.
Adding torques arithmetically without direction.
Put it right: Assign opposite signs to clockwise and anticlockwise torques and find the resultant.
Mixing up I and α with linear m and a: the correction is to use T = Iα for rotation and keep the axis consistent throughout the calculation.
Exam tips
- Draw a diagram showing the axis, each force and its perpendicular distance before substituting into T = Fr.
- State the direction convention for torques, then calculate the resultant torque before using T = Iα.
- Check units: torque in N m, I in kg m² and α in rad s⁻², and convert degrees to radians where needed.
Try the lesson
The start of the Torque and angular acceleration (A-level only): T = Fr T = Iα lesson, made from checked teaching notes for this specification point.
Have a go first
A force of 12 N acts at a perpendicular distance of 0.50 m from the axis of a rotating wheel. What is the torque about the axis?
Listen
Torque (moment of a force) measures the turning effect of a force about an axis: T = Fr, where F is the force and r is the perpendicular distance from the axis to the line of action. For a rotating rigid body, the resultant torque produces angular acceleration according to T = Iα, where I is the moment of inertia and α is angular acceleration in rad s⁻². These equations are the rotational analogues of F = ma and the moment equation. To solve problems, identify the axis, find the perpendicular distance, calculate resultant torque, then use T = Iα to find α, or combine with rotational kinematics. A strong answer earns marks for these points. Torque is defined by T = Fr, where r is the perpendicular distance from the axis to the line of action of the force, not necessarily the length of the object. The rotational form of Newton's second law is T = Iα, where I is the moment of inertia about the chosen axis and α is angular acceleration in rad s⁻². For several forces, calculate the resultant torque by taking clockwise and anticlockwise contributions with opposite signs before applying T = Iα. Moment of inertia depends on mass and its distribution about the axis, so the same torque produces different angular accelerations for different bodies or axes. A common slip: Using the full length of a rod as r when the force is not perpendicular to it. Instead, use the perpendicular distance from the axis to the line of action, or resolve the force. Exam tip: Draw a diagram showing the axis, each force and its perpendicular distance before substituting into T = Fr.
See it
Put it in order
Put these steps in the order they happen.
- 1. Combine with rotational kinematics, or use a = rα to link to linear acceleration
- 2. Apply T = Iα to find angular acceleration α
- 3. Calculate torque using T = Fr
- 4. Resultant torque
- 5. Identify the axis
- 6. Find the perpendicular distance from the axis to the line of action
- 7. Several forces? Take clockwise and anticlockwise contributions with opposite signs
Key words
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Torque
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Rotational form of Newton's second law
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Moment of inertia
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Angular acceleration
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See every definition
- Torque
- Measures the turning effect of a force about an axis, given by T = Fr, where r is the perpendicular distance from the axis to the line of action.
- Rotational form of Newton's second law
- The resultant torque produces angular acceleration according to T = Iα, the rotational analogue of F = ma.
- Moment of inertia
- Depends on mass and its distribution about the axis, so the same torque produces different angular accelerations for different bodies or axes.
- Angular acceleration
- Links to linear acceleration at a point by a = rα, allowing rotational and linear dynamics to be combined.
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