Angular Velocity — Ceiling Fan Speed (Worked Example)

Given

• f = 240 rev/min

Find

ω in rad/s.

Principle

Each revolution is 2π radians; convert rev/min to rev/s, then multiply by 2π.

Formula

Solution

1. Convert to rev/s: $f = 240/60 = 4\ \mathrm{rev/s}$

2. Multiply by radians per revolution: $\omega = 2\pi \times 4$

3. Compute: $\omega = 8\pi \approx 25.1\ \mathrm{rad/s}$

Unit check

rev/s × rad/rev = rad/s — correct.

What this means physically

25 rad/s means the blade tip of a 0.6 m fan sweeps at v = ωr ≈ 15 m/s (~54 km/h) — which is why fan blades move serious air despite looking lazy.