Question

A disk of a radius 50 cm rotates at a constant rate of 100 rpm. What distance in meters will a point on the outside rim travel during 30 seconds of rotation? ​ ​

Answer 1

The point will travel a distance of 15708 centimeters in 30 seconds of rotation.

Step-by-step explanation:

In this case, we see a disk rotating at constant rate, the travelled distance of a point on the outside rim (
`s`), in centimeters, is determined by using this expression:

`s = \omega \cdot r\cdot t` (1)

Where:

`\omega` - Angular speed, in radians per second.

`r` - Radius of the disk, in centimeters.

`t` - Time, in seconds.

If we know that
`\omega \approx 10.472\,(rad)/(s)`,
`r = 50\,cm` and
`t = 30\,s`, then the travelled distance of the point is:

`s = \omega \cdot r\cdot t`

`s = 15708\,cm`

The point will travel a distance of 15708 centimeters in 30 seconds of rotation.