Chapter 4, Problem 18CR

a.

To determine

To find: The angular speed in radians per minutes.

Answer to Problem 18CR

The angular speed is $672\pi \mathrm{radians}\mathrm{per}\mathrm{minute}$ .

Explanation of Solution

Given information: Given diameter of wheel is $28\mathrm{inches}$ and rotate at $336$ revolutions per minute.

Calculation:Given diameter of wheel is $28\mathrm{inches}$ and rotate at $336$ revolutions per minute.

Angle swept in one revolution $={360}^{\circ }$ .

Convert angle in radian:

  $={360}^{\circ }\times \frac{\pi }{{180}^{\circ }}=2\pi$

Angle swept in $336$ revolution $=2\pi \times 336=672\pi$ .

Angular speed $=\frac{\theta }{t}=\frac{672\pi }{1}=672\pi$ .

Thus, the angular speed is $672\pi \mathrm{radians}\mathrm{per}\mathrm{minute}$ .

b.

To determine

To find: The linear speed in inches per minutes and miles per hour.

Answer to Problem 18CR

The linear speed in $\mathrm{inches}\mathrm{per}\mathrm{minute}$ is $29568$ and $\mathrm{miles}\mathrm{per}\mathrm{hour}$

  $27.99$ .

Explanation of Solution

Given information: Given diameter of wheel is $28\mathrm{inches}$ and rotate at $336$ revolutions per minute.

Calculation:Given diameter of wheel is $28\mathrm{inches}$ and rotate at $336$ revolutions per minute.

Radius of wheel $\frac{28}{2}=14\mathrm{inches}$ .

Distance cover in $1$ revolution is :

  $\begin{array}{l}=2\pi r\\ =2\times \frac{22}{7}\times 14\\ =88\mathrm{inches}\end{array}$

Distance cover in $336$ revolution is $=88\times 336=29568\mathrm{inches}$ .

Linear speed $=\frac{s}{t}=\frac{29568}{1}=29568\mathrm{inches}\mathrm{per}\mathrm{minute}$ .

Linear speed in $\mathrm{inches}\mathrm{per}\mathrm{hour}$

  $=29568\times 60=1774080$ .

Linear speed in $\mathrm{miles}\mathrm{per}\mathrm{hour}$

  $=1774080\times 1.578\times {10}^{-5}=27.99$ .

Thus, the linear speed in $\mathrm{inches}\mathrm{per}\mathrm{minute}$ is $29568$ and $\mathrm{miles}\mathrm{per}\mathrm{hour}$

  $27.99$ .