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

Answer:

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

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 $\omega \approx 10.472\,\frac{rad}{s}$, $r = 50\,cm$ 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.