Chapter 11, Problem 3A

How do clockwise and counterclockwise torques compare when a system is balanced?

To determine

The comparison between the clockwise and counterclockwise torques when a system is balanced.

Answer to Problem 3A

They must be equal in magnitude for the given condition.

Explanation of Solution

Introduction:

The torque acting about an axis of rotation due to the force $F$ is given by,

  $\begin{array}{c}\tau =F\times \left(\text{lever arm}\right)\\ =F\left(\text{lever arm}\right)\sin \theta \end{array}$

Where,

  $\text{lever arm=}$ denotes the shortest distance of the point of application of force from the axis of rotation.

  $\theta =$ angle between the force and the lever arm

Now, when a system is balanced, it means that no torque act on a system. Hence, the clockwise and the counterclockwise torque must cancel each other, and thereby they should be equal in magnitude.

Conclusion:

Hence, the clockwise and counterclockwise torque acting on a system must be equal in magnitude if the system is balanced.