Uniform Circular Motion

Question

Suppose a piece of dust is stuck to a CD such that it does not slip even when the CD is spinning.

If the constant spin rate of the CD is 460 rpm, then what angular distance, in radians, is traveled by the piece of dust in 2.7 minutes?  

Answer 1

First, we want to figure out how many times the piece of dust rotates on the disk. So we can think of it as converting taking the number of rotations and multiplying it by the time in question.

460 rotations/min *2.7 min =1,242 rotations

And of course, we can check the answer with units.

So one rotation is equal to 360º which is 2π radians.

1,242 * 2π = 2484π radians

This is how many radians the dust traveled and thus the total angular distance.