Angular Velocity — Merry-Go-Round (Worked Example)

Given

• v = 3.0 m/s

• r = 2.0 m

Find

Angular velocity ω.

Principle

Linear and angular speed are linked by v = ωr — every point on a rigid rotator shares one ω.

Formula

Solution

1. Rearrange: $\omega = v/r$

2. Substitute: $\omega = 3.0 / 2.0$

3. Divide: $\omega = 1.5\ \mathrm{rad/s}$

Unit check

(m/s) ÷ m = 1/s = rad/s — correct.

What this means physically

1.5 rad/s is about one revolution every 4.2 s — a brisk but comfortable ride. A child halfway in (r = 1 m) moves at only 1.5 m/s with the same ω.