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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!

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However obvious it may seem, you should always do the following sanity check on physics problems: make sure your answer is in the right units!

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.

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Thanks for your help Kevin Carlson! – user46258 Oct 28 '12 at 1:42

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