Chapter 4.1, Problem 64E

a.

To determine

Find the angular speed of the carousel.

Answer to Problem 64E

The angular speed of the carousel is $25.133\text{radians/minute}$ .

Explanation of Solution

Given:

The carousel revolution time is $4$ revolutions/minute.

Calculation:

Find the angular speed.

  $\begin{array}{l}1\text{revolution}=\text{2}\pi \text{radians}\\ \theta =4\text{revolutions}\times \text{2}\pi \\ \omega =\frac{\theta }{t}=\frac{4\text{revolutions}\times \text{2}\pi }{\text{minute}}\approx 25.133\text{radians/minute}\end{array}$

Hence theangular speed of the carouselis $25.133\text{radians/minute}$ .

b.

To determine

Find the linear speed of the carousel.

Answer to Problem 64E

The linear speed of the carousel is $628.319\text{feet}/\text{minute}$ .

Explanation of Solution

Given:

The carousel revolution time is $4$ revolutions/minute.

Calculation:

  $\begin{array}{l}1\text{revolution}=\text{2}\pi \text{radians}\\ \theta =4\text{revolutions}\times \text{2}\pi \end{array}$

Radius of the carousel $=\frac{\text{Diameter}}{2}=\frac{50}{2}=25$ feet

  $\begin{array}{l}\text{Linear}\text{speed}=\frac{s}{t}=\frac{r\theta }{t}\\ =\frac{25\text{feet}\times 4\text{revolutions}\times \text{2}\pi }{\text{minute}}\\ \approx 628.319\text{feet}/\text{minute}\end{array}$

Hence thelinear speed of the carouselis $628.319\text{feet}/\text{minute}$ .