Chapter 8, Problem 54A

To determine

The angular velocity of the tire in rad/s.

Answer to Problem 54A

  $51.12\text{rad/s}$

Explanation of Solution

Given:

Linear velocity of the truck’s tire, $v=23\text{m/s}$

Radius of the tire of the truck’s tire, $r=45\text{cm = }0.45\text{m}$

Formula used:

For a rotating and rigid object, its linear velocity( v ) can be related to its angular velocity $\left(\omega \right)$ as,

  $v=r\omega$

Where r is the radius of the object.

Calculation:

Using the given values in above formula, the angular velocity of the tire will be,

  $\begin{array}{c}\omega =\frac{v}{r}\\ =\frac{23}{0.45}\\ =51.12\text{rad/s}\end{array}$

Conclusion:

Thus, the angular velocity of the truck is $51.12\text{rad/s}$ .