4.1.4

# Moments

Test yourself

## Moments

The moment of a force is the turning effect it creates.

### Equation

• The moment of a force is described by the equation:
• Moment (Nm) = force (N) × perpendicular distance from the point to the line of action of the force (m)
• m = F × d

### Units

• The units of moments are Newton metres (Nm).

### Example

• Doors open more easily if we press (exert force) far away from the hinge, rather than next to the hinge.
• Pushing further away from the hinge (fixed point) with the same force means the moment will be larger and the door will open more easily.

## Couples

A couple is a pair of equal and opposite coplanar forces. This means they lie in the same plane (coplanar), point in the opposite direction and have the same magnitude.

### No resultant force

• A couple has a turning effect but no resultant force.
• Remember, the two forces in a couple are equal and opposite.

### Moment of a couple

• Couples produce a turning effect and therefore a moment.
• The moment of a couple is defined by the equation:
• moment of a couple = force × perpendicular distance between the lines of action of the forces.
• m = F × d
• Remember the 'force' in this equation refers to one of the forces in the couple - don't add them together!

## Principle of Moments

The principle of moments states that in order for an object to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments.

### Example

• Consider the moments on the bar in the diagram.
• sum of anticlockwise moments = (5 × 2) + (10 × 4) = 50 Nm
• sum of clockwise moments = F × 2 = 2F Nm

### Example cont.

• For this object to be in equilibrium (not turning):
• 2F = 50 Nm
• F = 50 Nm ÷ 2 m
• F = 25 N