Moments

​​In a nutshell

The moment of a force measures the turning effect or rotational effect of a force on a body. The size of the object, the location of the force applied and the direction of the force all contribute to the turning effect on the object.

Equations

Variable definitions

Calculate a moment

If the force and the distance from the pivot are perpendicular, calculate the moment by multiplying the force by the distance. State whether the direction of the moment is clockwise or anti-clockwise.

​$$moment = F \times d$$​​

Example 1

Calculate the moment of the force about the pivot.

​$$\begin {aligned}moment &= F \times d \\&= 15 \times 0.2 \\&= \underline{3 \space Nm \space \space clockwise}\end {aligned}$$​​

Calculate a moment when the distance is not perpendicular

If the force and the distance from the pivot are not perpendicular, use trigonometry to find the perpendicular distance. Use the formula

​$$moment = F \times d \sin \theta$$​​

Example 2

Calculate the moment of the force about the pivot.

​$$\begin{aligned}moment &= F \times d \sin \theta \\&= 12 \times 5 \sin 30 \\&= \underline{30 \space Nm \space \space anti-clockwise}\end{aligned}$$​​