Chapter 6.2, Problem 27E

To determine

To convert: the units of angular velocity into revolutions per minute (rpm).

Answer to Problem 27E

  $811.7\text{ revolutions per minute}$

Explanation of Solution

Given information:

  $\text{Angular velocity}\left(\omega \right)=85\text{ radians per second}$

Calculation:

The angular velocity $\left(\omega \right)$ in rpm is evaluated as follows:

  $\begin{array}{c}\omega =85\text{ radians per second}\\ =\frac{\text{85 radians}}{\text{1 second}}\times \frac{\text{1 revolution}}{2\pi \text{ radians}}\times \frac{\text{60 second}}{\text{1 minute}}\left[\text{Changing the units}\right]\\ =\frac{85\times \text{60}}{2\pi }\times \frac{\text{1 revolution}}{\text{1 minute}}\\ =811.7\text{ revolutions per minute}\end{array}$

Thus the angular velocity is 811.7 revolutions per minute.