# Angular Velocity of a Pulley

I am having trouble with this questions about angular velocity. Could you please show me the solution? I keep getting ≈ $41.9$ cm/sec but my friend gets ≈ $419$ cm/sec.

Question: A pulley of radius $10$ cm rotates $40$ times a minute. Find the angular velocity of the pulley in radians per second.

My solution: $ω = 40 \text{ times}/60 \text{ seconds}$ and $r = 10$.

Convert $ω$ to radians per second $(2π)(40/60) = 4π/3$ radians/sec

Angular Velocity $= rω = 10(4π/3) ≈ 40π/3$ cm/sec $≈ 41.9$ cm/sec

Your computation gives the speed of a particle sitting on the outside edge of the pulley. The angular velocity is unrelated to the size of the rotating body: your $4\pi/3$ is the answer.