**Moment of force**

The turning effect of force is called moment of force.

The moment of force depends on the following factors.

The size (magnitude) of the force

The perpendicular distance between the line of action of the force and the turning point which is called the pivot.

We calculate the moment of force by using the following formula

Moment of force = force * perpendicular distance from pivot to the line of action of the force

Moment=F * d

Moment is measured in newton meters(**Nm**).

One force *on its own* isn’t much use to us. We normally look at situations where turning effects are **balanced** (or not!).

Let’s look at the example below and find the missing force *F*:

If the system is balanced, the anticlockwise turning effect of force F must equal the clockwise turning effect:

*clockwise moment = anticlockwise moment*

Clockwise moment = 5 N × 0·50 m = **2·50 Nm**.

Anticlockwise moment = F × 0·25 m = 2·50 Nm

Force F = 2·50 Nm ÷ 0·25 m = 10 N

In order to balance the 5 N force acting at 0·5 m from the pivot, we require 10 N acting in the opposite direction but at 0·25 m.

*Unbalanced Forces*

Sometimes moments can easily become unbalanced – even when we don’t want them to!

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In these unfortunate examples, it would seem that in **loading** the cart, some of the boxes must have slipped to the back – *further away* from the pivot – greatly increasing their turning effect. In the case of the lorry, its weight wasn’t enough to balance the heavy bricks.

The result was the lifting of the donkey – who must have been very surprised! For the lorry, it was lucky nobody was hurt.

<p><a href=”http://vimeo.com/22743057″>Moments (turning effects of forces)</a> from <a href=”http://vimeo.com/user2127784″>Mr Ong</a> on <a href=”http://vimeo.com”>Vimeo</a>.</p>Sometimes **more than one** force acts on the **same side** of the pivot. Their overall *turning effect* is easy to work out.

The 2 N force has a moment of 2 × 0·2 m = 0·4 Nm clockwise.

The 5 N force has a moment of 5 × 0·5 m = 2·5 Nm clockwise.

Their combined moment = 0·4 Nm + 2·5 Nm = 2·9 Nm clockwise.

Moments can just be added, but they **must** act in the same direction.

**principle of moments.**

**Principle of Moments.**Lets take a challenge to reinforce your understanding. When you try the following challenge, calculate the clockwise and anti-clockwise moment before clicking on “Release”

# Moments Summary

The turning effect (or moment) of a force is given by:

*moment = force × perpendicular distance from pivot*

The normal units used for force and distance are newtons andmetres respectively, so the usual unit for moment is the newton-metre (**Nm**)

Another name for a pivot is fulcrum.

Moments can either be *clockwise* or *anticlockwise*.

When more than one force acts in the same direction, their overall turning effect is just the **sum** of their moments.

When forces act in a different direction, yet still balance, the total turning effect in each direction will be the same:

*sum of clockwise moments = sum of anticlockwise moments*

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Taking a QUIZ about this lesson

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