Question

A 0.25 m diameter grinding wheel rotates at 2500 rpm. Calculate it's angular velocity in rad/s.

Answer 1

Answer on Question#39162, Physics, Mechanics

A 0.25 m diameter grinding wheel rotates at 2500 rpm. Calculate it's angular velocity in rad/s.

Solution:

Revolutions per minute (abbreviated rpm) are a measure of the frequency of a rotation. It annotates the number of turns completed in one minute around a fixed axis.

Because of the measured physical quantity, the formula sign has to be $f$ for (rotational) frequency and $\omega$ for angular velocity.

$$1 \mathrm{rad/s} = \frac{60}{2\pi} \mathrm{rpm} = \frac{1}{2\pi} \mathrm{Hz}.$$

The conversion between a frequency $f$ measured in hertz and an angular velocity $\omega$ measured in radians per second are:

$$\omega = 2 \pi f$$

We have $f = 2500 \, \mathrm{rpm} = 2500 / 60 = 41.67 \, \mathrm{Hz}$

$$\omega = 2 \pi f = 2 \cdot 3.14 \cdot 41.67 = 261.7 \, \mathrm{rad/s}$$

Answer. 261.7 rad/s.