Chapter 8, Problem 58A

To determine

The linear velocity of a point $7.00\text{cm}$ from the center of the wheel.

Answer to Problem 58A

  $0.175\text{m/s}$

Explanation of Solution

Given:

Angular velocity of the wheel, $\omega =2.50\text{rad/s}$

The point is $7.00\text{cm}$ away from the center.

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 linear velocity of a point $7.00\text{cm}$ , or $0.07\text{m}$ , from the center of the wheel will be,

  $\begin{array}{c}v=r\omega \\ =0.07\times 2.5\\ =0.175\text{m/s}\end{array}$

Conclusion:

Thus, the linear velocity of a point $7.00\text{cm}$ from the center of the wheel is $0.175\text{m/s}$ .