Edexcel A-Level Physics 9PH0
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Mechanics
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Further Mechanics
Angular velocity, period and frequency of rotation
- 2 things to know
- Papers 1 and 3
Overview
Recall questions on v = ωr, the relationships between angular velocity, period and frequency, and comparing two points at different radii on one disc.
What you need to know
Answer each one before you reveal it.
How do you convert a number of complete revolutions into an angular displacement in radians?
Questions from this subtopic
Each one with the model answer underneath.
- 1
How does v = ωr follow from the definitions of angular velocity and arc length?
Model answer
In a time t the object sweeps an angle θ = ωt and travels an arc s = rθ = rωt, so its linear speed is v = s/t = ωr.
- 2
State the relationship between the period of circular motion and angular velocity:
Model answer
The period is T = 2π/ω, because one complete revolution corresponds to an angular displacement of 2π rad.
- 3
How is angular velocity related to frequency of rotation?
Model answer
Angular velocity is ω = 2πf, since the frequency is the reciprocal of the period.
- 4
Two points sit at different radii on the same rotating disc. How do their angular velocities and their linear speeds compare?
Model answer
Both points have the same angular velocity because they sweep the same angle in the same time, but the point at the larger radius has the greater linear speed since v = ωr.
- 5
A wheel turns at 300 revolutions per minute. What is its angular velocity?
Model answer
300 revolutions per minute is 5.0 revolutions per second, so ω = 2π × 5.0 = 31 rad s⁻¹.
- 6
A car wheel of radius 0.32 m rolls without slipping while the car travels at 24 m s⁻¹. What is the wheel's angular velocity?
Model answer
Rearranging v = ωr gives ω = 24 ÷ 0.32 = 75 rad s⁻¹.
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