Torque – Learn

Torque (\tau) is the rotational effect that a force has on an object. The rotational effect occurs around some fixed point called a pivot. Torque is a vector quantity and the direction is described as being clockwise or anticlockwise.

The amount of torque that a force generates around the pivot point depends on several factors:

  • magnitude of the applied force
  • the distance from the pivot that the force is applied 
  • the direction that the force is applied

If the applied force is at right angles to the line between the pivot point and the force, torque, (\tau), is given by the formula:



\tau is the torque in Nm

F is the applied force in N

r is the distance between the pivot point and the point where the force is applied in m

Often, the force is not applied at right angles and in these situations, it is only the component of the force that is perpendicular to the line between the pivot and the applied force that results in torque.

For these situations, we derive the following formula:

\tau ={ F }_{ \bot }r

\tau ={ F }r\sin { \theta }

Example 1:

A perpendicular force of 10N is applied to a spanner that is 45cm long. What is the magnitude of the torque that is generated?



\tau =10\times 0.45

\tau =4.5\:Nm

Example 2:

A force of 200N is applied to an industrial door that is 5m wide at an angle of 30° as shown below. Calculate the torque that is generated:


\tau ={ F }r\sin { \theta }

\tau ={ 200 }\times 5\times \sin { { 30 }^{ \circ } }

\tau =500\:Nm