Chapter 10, Problem 5A

At a given distance from the axis, how does linear (or tangential) speed change as rotational speed changes?

To determine

The relation between the linear speed and rotational speed for a given distance from the axis.

Answer to Problem 5A

For the fixed distance from the axis, the linear speed is directly proportional to the rotational speed.

Explanation of Solution

Introduction:

A linear speed $\left(v\right)$ is written in terms of the rotational speed $\left(\omega \right)$ as,

  $v=r\omega$

Where, $r=$ distance from the axis

As can be seen from above equation, if the distance from the axis is fixed, the linear speed changes linearly with the rotational speed.

Conclusion:

Hence, the linear speed and rotational speed are directly proportional to each other for the fixed distance from the axis.