Chapter 6.2, Problem 23E

To determine

To find: the angular velocity (round to the nearest tenth).

Answer to Problem 23E

  $39.3\text{ radians per minute}$

Explanation of Solution

Given information:

Angular displacement $\left(\theta \right)$ = 100 revolutions

Time $\left(t\right)$ = 16 minutes

Calculation:

Convert the angular displacement into radian by multiplying the number of revolutions by $2\pi$ as shown below.

  $\begin{array}{c}\theta =100rev\left(\frac{2\pi }{1rev}\right)\\ =200\pi \text{ radians}\end{array}$

Now evaluate the angular velocity $\left(\omega \right)$ as follows:

  $\begin{array}{l}\omega =\frac{\theta }{t}\\ =\frac{200\pi }{16}\left[\text{Put the values of }\theta \text{ and }t\right]\\ =39.3\text{ radians per minute}\end{array}$

Thus the angular velocity is 39.3 radians per minute.