I am having trouble with this questions about angular velocity. Could you please show me the solution? I keep getting $\approx 41.9$ cm/sec but my friend gets $\approx 419$ 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: $\omega = 40 \text{ times}/60 \text{ seconds}$ and $r = 10$.
Convert $ω$ to radians per second $(2\pi)\times\frac{40}{60} = \frac{4\pi}{3}$ radians/sec
$\text{Angular Velocity} = r\omega = 10\times\frac{4\pi}{3} \approx \frac{40\pi}{3}$ cm/sec $\approx 41.9$ cm/sec
Please help!