Angular Velocity — Spinning CD (Worked Example)

Given

• f = 300 rev/min

Find

Angular velocity ω in rad/s.

Principle

One revolution is 2π radians and one minute is 60 s, so ω = 2π × (rev/s).

Formula

Solution

1. Convert to rev/s: $f = 300/60 = 5\ \mathrm{rev/s}$

2. Multiply by $2\pi$: $\omega = 2\pi \times 5$

3. Calculate: $\omega = 31.4\ \mathrm{rad/s}$

Unit check

rev/s × rad/rev = rad/s — correct.

What this means physically

31.4 rad/s — the disc's edge (r = 6 cm) sweeps past at v = ωr ≈ 1.9 m/s. Optical drives spin fastest when reading the inner tracks to keep the linear speed constant.