11.7   Torque

Suppose a force is applied at point as shown in the figure above. Point is part of a rigid body with an axis of rotation going through point . Suppose the angle between the force and the position vector is . The force can be decomposed into which does not produce rotation and which does produce rotation about the origin . The component is given by

This component produces a torque whose magnitude is given by

The unit for the torque is . Note that torque is a vector quantity.

Another way to look at the torque equation is to consider the following

where is called the moment arm.

If more than one force is acting on a rigid body, the net torque (or resultant torque) is

By definition, a force that tends to rotate the object clockwise has a negative torque, while a force that tends to rotate the object counterclockwise has a positive torque.

 

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