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#### Calculating moments

*Factors affecting moments*

When you push a door closed, it doesn't travel in a straight line - it **turns** around the hinges. This is an example of a **moment (or torque).**

**So there are three things that are important:**

- The size of the force.
- The direction of the force.
- The distance from the force to the hinge.

#### Definition of Moments (or Torque)

**"A moment is defined as a force multiplied by the perpendicular distance from the line of action of the force to the pivot."**

**Units:** Nm. Symbol, M (or sometimes T)

#### Principle of Moments

*For equilibrium:*

The sum of the clockwise moments about a point = sum of the anticlockwise moments about that point.

#### Couples

**If you have two forces (for instance, a couple of forces) acting on an object and the forces are:**

- parallel
- in opposite directions
- of equal size
- not along the same line of action

...you have got a couple.

#### Equilibrium Conditions

You need to check that two conditions are satisfied before you can say that something is in **equilibrium.**

- The sum of the forces in any direction = 0. If this is satisfied, the object will have no linear acceleration (for instance, it won't accelerate in any direction).
- The sum of the moments about any point (not just the pivot point) = 0. If this is satisfied, there is no angular (or circular) acceleration (for instance, the object won't rotate faster or slower.)

**We write these two in short hand as:**

Σ F = 0

Σ M = 0

#### Triangle of Forces

This is a quick way of finding out if the forces acting on an object are in **equilibrium.**

This object experiences three forces.

If it is in equilibrium then drawing accurate vector diagrams of each force one after the other will produce a **closed triangle.**

#### Centre of Gravity (and Centre of Mass)

*Why is it useful?*

When doing moment calculations you can say that all the weight of an object acts through the Centre of Gravity.

#### What's the difference between Centres of Gravity and Mass?

**Centre of Gravity** = the point where all the weight seems to be concentrated.

**Centre of Mass** = the point where all the mass seems to be concentrated.

#### Where can you find the Centre of Gravity?

For **regular shapes** it is the geometrical centre of the object - for example, the centre of a cube or a sphere.

For **irregular shapes**, hang the object from a point on its edge and the Centre of Gravity will end up vertically below the point you are hanging it from.