Chapter 4.1, Problem 65E

(a)

To determine

Find the angular speed of the carousel .

Answer to Problem 65E

The angular speed of the carousel is 25.133 radians per minute

Explanation of Solution

Consider,

  $d=50foot$

So $r=\frac{d}{2}=25foot$

Each revolution generates 2p radians. It follows that in 4 turns, a carousel turns $\left(4\right)\left(2\pi \right)=8\pi$ radians per minute

Angular speed is,

  $\begin{array}{cc}\omega & =\frac{\theta }{t}\\ & =\frac{8\pi \text{radian}}{1\text{minute}}\end{array}$

=25.133 radians per minute

Hence the angular speed of the carousel is 25.133 radians per minute

(b)

To determine

Find the linear speed of the platform rim of the carousel.

Answer to Problem 65E

The linear speed of the carousel is 628.32 foot per minute

Explanation of Solution

Given:

Consider,

  $d=50foot$

So $r=\frac{d}{2}=25foot$

Each revolution generates 2p radians. It follows that in 4 turns, a carousel turns $\left(4\right)\left(2\pi \right)=8\pi$ radians per minute

The linear speed is,

  $\begin{array}{cc}v& =\frac{s}{t}\\ & =\frac{r\theta }{t}\\ & =\frac{25\times 8\pi \text{foot}}{1\text{min}}\\ & =200\pi \end{array}$

  $v=628.32$ foot per minute

Hence the linear speed of the carousel is 628.32 foot per minute