Question

A record rotates on a turntable at 45 rpm. what is the angular speed in rad/s

Answer 1

45 rpm corresponds to 45 revolutions per minute.

In order to convert into rad/s, we should keep in mind that:

`1 rev = 2 \pi rad`

`1 min = 60 s`

so, the factor of conversion between rpm and rad/s is:

`1 (rev)/(min) = (2 \pi rad/rev)/(60 s/min)=0.105 (rad)/(s)`

so, the angular speed converted in rad/s becomes:

`\omega = 45 (rev)/(min) \cdot 0.105 =4.72 rad/s`