Chapter 6.4, Problem 63E

To determine

To find: the angular velocity..

Answer to Problem 63E

  $88\text{ radians per second}$

Explanation of Solution

Given information:

Angular displacement $\left(\theta \right)$ = 84 revolutions

Time $\left(t\right)$ = 6 seconds

Calculation:

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

  $\begin{array}{c}\theta =84rev\left(\frac{2\pi }{1rev}\right)\\ =168\pi \text{ radians}\end{array}$

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

  $\begin{array}{c}\omega =\frac{\theta }{t}\\ =\frac{168\pi }{6}\left[\text{Put the values of }\theta \text{ and }t\right]\\ =88\text{ radians per second}\end{array}$

Thus the angular velocity is 88 radians per second.