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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.

Your recallNot started
Numbers

How is angular velocity related to the period and to the frequency of rotation, and how do the angular velocities of two points at different radii on a rotating disc compare?

Process

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. 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. 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. 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. 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. 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. 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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