# A compact disc spins at a rate of 200 to 500 revolutions per minute. What are the equivalent...

## Question:

A compact disc spins at a rate of 200 to 500 revolutions per minute. What are the equivalent rates measured in radians per second?

## Angular Speed:

Let a body is rotating about an axis which covers an angle {eq}\theta {/eq} at time t.

Then the angular velocity of the body is {eq}\omega = \displaystyle \frac{\theta}{t} {/eq}

## Answer and Explanation:

Part 1:

The speed of the disk is 200 revolutions per minute.

{eq}\begin{align*} \omega_1 & =200 \ rpm \\\\ & = \frac{2\pi \times 200 }{60} \ rad/s \\\\ & = 20.93 \ rad/s \Rightarrow(Answer) \end{align*} {/eq}

Part 2:

The speed of the disk is 500 revolutions per minute.

{eq}\begin{align*} \omega_2 & =500 \ rpm \\\\ & = \frac{2\pi \times 500 }{60} \ rad/s \\\\ & = 52.3 \ rad/s \Rightarrow(Answer) \end{align*} {/eq}