Chapter 1, Problem 1.1Q

What is torque? What role does torque play in the rotational motion of machines?

To determine

The definition of torque.

The role of torque in the rotational motion of machines.

Explanation of Solution

Torque is nothing but an influence which is required for twisting or rotating an object about its own axis. It is also known as Moment of Force. The SI unit of torque is Nm.

Consider a figure below:

  

The axis is known as ‘pivot point (O)’. if the force vector is ‘F’ which is acting at a distance ‘r’ from the point O at an angle ‘ $\theta$ ’, then the torque will be

  $\begin{array}{l}\tau =r\times F\\ \tau =rF\sin \theta \end{array}$

In linear motion, a force acting on any object alters the speed of the object. Similarly, in case of rotational motion, the torque increases the speed of the rotating object. In simple words, the force in the linear motion is analogous to torque in rotational motion.

Consider a cylinder which is free to rotate around its axis. If a force is applied such that the line of action passes through the center of the cylinder, the cylinder will not rotate. If the same force is applied to the right, then it will start rotating in the counter - clockwise direction. Hence, the rotation does not depend on magnitude only but also on the direction.

For instance, let the force is applied along the axis of rotation:

  

The force is applied such that the line of action misses the axis of rotation: