Angular velocity

Overview

Recall questions on the definition of angular velocity and its unit, the relations ω = 2πf and ω = 2π/T, the link v = rω and its derivation from the radian, and worked calculations for points at different radii on a rotating body.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Define angular velocity.

   Model answer

   Angular velocity is the rate at which the angular position of a body changes, that is the angle swept out per unit time.

2. 2

   State the unit of angular velocity.

   Model answer

   Angular velocity is measured in radians per second, rad s⁻¹.

3. 3

   State the equations linking angular velocity to period and to frequency.

   Model answer

   The relations are ω = 2π/T and ω = 2πf, where ω is in rad s⁻¹, T is the period in s and f is the frequency in Hz.

4. 4

   State the equation linking linear speed and angular velocity in circular motion, defining each symbol and its unit.

   Model answer

   The equation is v = rω, where v is the linear speed in m s⁻¹, r is the radius of the circular path in m and ω is the angular velocity in rad s⁻¹.

5. 5

   Show that v = rω follows from the definition of the radian.

   Model answer

   An arc of length s subtends an angle θ = s/r, so dividing both sides by time gives θ/t = (s/t)/r, and since θ/t is ω and s/t is v the result is v = rω.

6. 6

   A wheel of radius 0.330 m rotates with an angular velocity of 8.00 rad s⁻¹. Calculate the linear speed of a point on the rim.

   Model answer

   The linear speed is 0.330 × 8.00 = 2.64 m s⁻¹ along the tangent. Dividing 2.64 m s⁻¹ by 0.330 m returns 8.00 rad s⁻¹.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.