AQA · A-Level · Physical Education
Course version: 7582 · Version from Sept 2016
Angular displacement, angular velocity, angular acceleration.
Full specification wording
Angular motion: Angular displacement, angular velocity, angular acceleration.
These three quantities form a chain of rates.
Checked against the AQA 7582 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
These three quantities form a chain of rates. Angular displacement θ is the angle turned about an axis, in radians. Angular velocity ω is how fast that angle changes, ω = Δθ/Δt, in rad s⁻¹. Angular acceleration α is how fast angular velocity changes, α = Δω/Δt, in rad s⁻². For a trampolinist completing a somersault, θ might be 2π rad for one rotation; dividing by the time of the rotation gives ω; if ω changes from 0 to that value during take-off, dividing by the take-off time gives α. A negative value shows rotation or change of rotation in the opposite direction to the chosen positive sense. In multiple-choice items, check the units and the direction sign before choosing.
What earns the marks
- Angular displacement θ is the angle turned about an axis, measured in radians.
- Angular velocity ω = Δθ/Δt is the rate of change of angular displacement, measured in rad s⁻¹.
- Angular acceleration α = Δω/Δt is the rate of change of angular velocity, measured in rad s⁻².
- A change in angular velocity over time produces angular acceleration, including when a rotating body slows down.
- The sign of an angular quantity indicates the direction of rotation relative to a chosen positive sense.
- Calculations require consistent radian measure and a stated axis of rotation.
Common mistakes and how to put them right
Treating angular displacement as a linear distance.
Put it right: θ is an angle in radians.
Assuming angular acceleration only occurs when a body speeds up.
Put it right: Any change in ω over time, including slowing, is angular acceleration.
Dividing degrees by seconds and labelling the answer rad s⁻¹.
Put it right: Convert to radians first, then divide by time.
Ignoring the sign of ω or α.
Put it right: State the positive sense and keep signs consistent.
Exam tips
- Write the defining equation before substituting values, so the quantity being found is clear.
- Convert all angles to radians at the start of a calculation to avoid unit errors.
- Use the sign of the answer to describe direction, and state the positive sense you have chosen.
Try the lesson
The start of the Angular motion: Angular displacement, angular velocity, angular acceleration. lesson, made from checked teaching notes for this specification point.
Have a go first
A gymnast rotates through 90° during a swing on the high bar. What is this angular displacement expressed in radians?
Listen
These three quantities form a chain of rates. Angular displacement θ is the angle turned about an axis, in radians. Angular velocity ω is how fast that angle changes, ω = Δθ/Δt, in rad s⁻¹. Angular acceleration α is how fast angular velocity changes, α = Δω/Δt, in rad s⁻². For a trampolinist completing a somersault, θ might be 2π rad for one rotation; dividing by the time of the rotation gives ω; if ω changes from 0 to that value during take-off, dividing by the take-off time gives α. A negative value shows rotation or change of rotation in the opposite direction to the chosen positive sense. In multiple-choice items, check the units and the direction sign before choosing. A strong answer earns marks for these points. Angular displacement θ is the angle turned about an axis, measured in radians. Angular velocity ω = Δθ/Δt is the rate of change of angular displacement, measured in rad s⁻¹. Angular acceleration α = Δω/Δt is the rate of change of angular velocity, measured in rad s⁻². A change in angular velocity over time produces angular acceleration, including when a rotating body slows down. A common slip: Treating angular displacement as a linear distance: the error is giving metres for a rotation. Instead, θ is an angle in radians. Exam tip: Write the defining equation before substituting values, so the quantity being found is clear.
See it
Put it in order
Put these steps in the order they happen.
- 1. Angular acceleration α = Δω/Δt (rad s⁻²)
- 2. Sign of ω or α gives direction relative to chosen positive sense
- 3. Angular velocity ω = Δθ/Δt (rad s⁻¹)
- 4. Angular displacement θ (radians)
Key words
Say what each word means before you turn the card.
Angular displacement
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Angular velocity
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Angular acceleration
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Sign of an angular quantity
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See every definition
- Angular displacement
- The angle turned about an axis, measured in radians.
- Angular velocity
- The rate of change of angular displacement, ω = Δθ/Δt, measured in rad s⁻¹.
- Angular acceleration
- The rate of change of angular velocity, α = Δω/Δt, measured in rad s⁻².
- Sign of an angular quantity
- Indicates the direction of rotation relative to a chosen positive sense.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
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