The **moment of a force** or torque, r is defined as the turning effect of the force about a pivot and is the product of the force (F) and the perpendicular distance (d) from the line of action of the force to the pivot.

- SI unit of moment of a force is Newton-metre (Nm). It is a vector quantity.
- Its direction is given by the right-hand grip rule perpendicular to the plane of the force and pivot point which is parallel to the axis of rotation.

$$r = F \times d$$

,where

r is the moment of force/torque

F is the force

d is the perpendicular distance from the line of action of the force to the pivot

## Couple

A couple is a pair of forces, equal in magnitude but opposite in direction, whose lines of motion do not coincide.

- Will still rotate as there is a net moment
- As forces are equal and opposite, resultant force is zero and so there is no linear acceleration
- $r = F \times d$

Torque(Moment of a couple) is the product of one of the forces and the perpendicular distance between their lines of action of the forces.

- Can take moment from any point

## Self-Test Questions

### Consider the figure above. Given that the cat weighs 150 N and the distance from the cat to the pivot is 30 cm, calculate the moment of force about the pivot.

**Show/hide answer**

$$\begin{aligned} r &= F \times d \\ &= 150 \times 0.30 \\ &= 45 \text{ Nm} \end{aligned}$$

### Why is it easier to open the lid of a container with a spoon than a coin?

**Show/hide answer**

A spoon is longer than a coin. If you use them to open the lid of a container by pivoting, the perpendicular distance (d) will be longer for a spoon than a coin.

Let’s assume that it takes an $x \text{ Nm}$ of moment of a force to open the lid and that $d_{\text{spoon}} = 2 d_{\text{coin}}$.

Find amount of force needed to open the lid if we use a **spoon**:

$$\begin{aligned} r &= F \times d \\ x &= F_{\text{spoon}} \times d_{\text{spoon}} \\ F_{\text{spoon}} &= \frac{x}{d_{\text{spoon}}} \end{aligned}$$

Find amount of force needed to open the lid if we use a **coin**:

$$\begin{aligned} r &= F \times d \\ x &= F_{\text{coin}} \times d_{\text{coin}} \\ F_{\text{coin}} &= \frac{x}{d_{\text{coin}}} \end{aligned}$$

Since $d_{\text{spoon}} = 2 d_{\text{coin}}$,

$$\begin{aligned} F_{\text{coin}} &= \frac{x}{\frac{d_{\text{spoon}}}{2}} \\ &= 2 \frac{x}{d_{\text{spoon}}} \\ &= 2 F_{\text{spoon}} \end{aligned}$$

From the calculations above ($F_{\text{coin}} = 2 F_{\text{spoon}}$), you will need twice as much force to open the lid of a container if you use a coin.

Waw Very Good

Nice note

thank

Auniform (m) rule balances when aknife edge is put at 58cm when 20g is at one end.at which end must weight be suspended

Perfect physics