# Moment Of A Force

Show/Hide Sub-topics (Forces & Turning Effect Of Forces | O Level Physics)
Show/Hide Sub-topics (Forces And Dynamics | A Level Physics)

## Turning Effect

If a body under the action of a net external force is allowed to rotate about a pivot, the body will tend to turn in the direction of the applied force.

## Examples Of Turning Effect Of Force

• A person pushing a swing will make the swing rotate about its pivot.
• A worker applies a force to a spanner to rotate a nut.
• A person removes a bottle’s cork by pushing down the bottle opener’s lever.
• A force is applied to a door knob and the door swings open about its hinge.
• A driver can turn a steering wheel by applying a force on its rim.

## Moment Of A Force

The principle of moment finds its most illustrative example in a basic lever, which consists of a rigid bar resting on a pivot or fulcrum. This simple mechanical device is employed to transfer a force into movement, effectively enabling the manipulation of a load.

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.
• The turning effect of the force (or moment of a force or torque) is proportional to:
• the perpendicular distance from the line of action of the force to the pivot
• the magnitude of the force
• A clockwise rotation about the pivot is a clockwise moment.
• An anticlockwise rotation about the pivot is an anticlockwise moment.

$$r = F \times d$$

,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

In order to create a moment of force, the line of action of the force must not pass through the pivot. As in this case, the $d$ will be 0 and hence, moment will be 0 as well.

## 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

## Worked Examples

### Example 1

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.

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

### Example 2

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

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.

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