Chapter 10, Problem 6A

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

To determine

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

Answer to Problem 6A

For the given rotational speed, the linear speed is directly proportional to the distance from the changes.

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 rotational speed is fixed, then the tangential speed changes linearly as the distance from the axis changes.

Conclusion:

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