Chapter 9.2, Problem 40E

(a)

To determine

To find: The radians for which the people rotate each second.

Answer to Problem 40E

The radian by which the people rotate each second is $\frac{\pi }{2}\text{radians}$ .

Explanation of Solution

Given:

The length of the centrifuge is 58 feet and spun at a rate of about 15 revolutions per minute.

Calculation:

Consider the spin revolution minute is,

  $15\times 360°$

The spin revolution per second is,

  $\frac{15}{60}\times 360°=90°$

Then, convert the degree into radian as,

  $\begin{array}{c}90°=90°\times \frac{\pi }{180°}\\ =\frac{\pi }{2}\text{radians}\end{array}$

(b)

To determine

To find: The length of the arc through which the people are rotated.

Answer to Problem 40E

The length of the arc is $45.6\text{ft}$ .

Explanation of Solution

Given:

The length of the centrifuge is 58 feet and spun at a rate of about 15 revolutions per minute.

Calculation:

Consider the radius of the centrifuge is obtained as,

  $\frac{58}{2}\text{ft}=29\text{ft}$

Then, the length of the arc is obtained as,

  $\begin{array}{c}S=29\left(\frac{\pi }{2}\right)\\ =45.553\\ =45.6\text{ft}\end{array}$