Physics

6.7 - Moments - The Turning Effect

9 min

What a moment is

Calculating a moment

Clockwise and anticlockwise moments

Balancing a seesaw

note 1 of 5

A moment is the turning effect of a force

When a force acts on an object that can turn about a fixed point (the pivot), it produces a turning effect called the moment of the force.
Everyday examples include pushing a door open, loosening a nut with a spanner, and using a wheelbarrow.

Formula for the moment of a force

$M = F d$

Where:

$M$ = Moment of the force, in newton metres (Nm)
$F$ = Force, in newtons (N)
$d$ = Perpendicular distance from the pivot to the line of action of the force, in metres (m)

A spanner gripping a nut labelled pivot, with a downward arrow labelled force at the end of the handle and a double arrow labelled perpendicular distance between the force and the pivot.

What changes the size of a moment

Larger force - Increases the moment.
Greater distance from the pivot - Increases the moment.
Angle of the force - Applying the force at right angles (90°) gives the largest moment. Any other angle reduces the perpendicular distance to the pivot.

Moments have a direction

A moment turns an object either clockwise or anticlockwise, depending on the direction of the force and which side of the pivot it acts on.

note 2 of 5

Worked example - Moment of a force on a nut

A spanner is used to undo a tight nut. A force of 50 N is applied to the spanner at a perpendicular distance of 0.3 m from the nut, which acts as the pivot. What is the moment of the force on the nut?

A spanner gripping a hexagonal nut, with a blue arrow pointing down from the end of the handle labelled 50 N and the distance to the nut marked 0.3 m.

Step 1 - Write down the values

Force, $F = 50$ N
Perpendicular distance, $d = 0.3$ m

Step 2 - Formula

$M = F d$

Step 3 - Substitution and calculation

$M = 50 \times 0.3 = 15 Nm$

The moment of the force on the nut is 15 Nm.

note 3 of 5

The principle of moments

An object that can turn about a pivot is balanced (in rotational equilibrium) when the turning effects on each side cancel out.
Principle of moments - When an object is balanced:

Total clockwise moment = total anticlockwise moment

If the clockwise and anticlockwise moments are not equal, there's a resultant moment and the object turns.

A beam balanced on a triangular pivot, with a 450 N weight 1 m to the left of the pivot and a 300 N weight 1.5 m to the right.

note 4 of 5

Worked example - Tension in a supporting rope

A uniform wooden beam 10 m long and weighing 1,600 N rests horizontally on a support 2 m from one end. A rope is attached vertically to the other end and holds the beam so that it balances. What is the tension in the rope?

The support acts as the pivot. The weight acts downwards at the centre of mass (the middle of the beam); the rope tension acts upwards at the far end.

A wooden beam on a pivot 2 m from its left end, with a 1,600 N arrow down at its centre and a rope at the right end pulling up with an unknown tension, the spans marked 2 m, 8 m and 10 m.

Step 1 - Find the perpendicular distances from the pivot

Centre of mass is at the middle of the 10 m beam - 5 m from each end. The pivot is 2 m from one end, so the weight acts 5 - 2 = 3 m from the pivot.
The rope is at the far end, 10 - 2 = 8 m from the pivot.

Step 2 - Apply the principle of moments

$W \times d_{W} = T \times d_{T}$

$1,600 \times 3 = T \times 8$

Step 3 - Rearrange and solve for T

$T = \frac{1,600 \times 3}{8} = 600 N$

The tension in the rope is 600 N.

note 5 of 5

Levers make it easier to do work

A lever is a rigid bar that turns about a pivot.
Levers act as force multipliers: since $M = F d$ , increasing the distance from the pivot means a smaller force can produce the same turning effect.
This is why a long spanner loosens a stiff nut more easily than a short one, and why a long crowbar can lift heavy loads.

A bar resting on a triangular pivot, with a weight and a downward arrow labelled force on the right and curved arrows labelled turning effect showing the bar turning about the pivot.

key terms

TermDefinition

MomentThe turning effect of a force, equal to the force multiplied by the perpendicular distance from the pivot to the line of the force.

PivotThe fixed point that an object turns about.

Principle of momentsWhen an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment.

LeverA rigid bar that turns about a pivot to act as a force multiplier.

end of notes

Key points to remember

A moment is the turning effect of a force

When a force acts on an object that can turn about a fixed point (the pivot), it produces a turning effect called the moment of the force.

Everyday examples include pushing a door open, loosening a nut with a spanner, and using a wheelbarrow.

Formula for the moment of a force

$M = F d$

Where:

M

= Moment of the force, in newton metres (Nm)

F

= Force, in newtons (N)

d

= Perpendicular distance from the pivot to the line of action of the force, in metres (m)

The principle of moments

An object that can turn about a pivot is balanced (in rotational equilibrium) when the turning effects on each side cancel out.

Principle of moments - When an object is balanced:

Total clockwise moment = total anticlockwise moment

If the clockwise and anticlockwise moments are not equal, there's a resultant moment and the object turns.

Worked example - Tension in a supporting rope

The support acts as the pivot. The weight acts downwards at the centre of mass (the middle of the beam); the rope tension acts upwards at the far end.

Levers make it easier to do work

A lever is a rigid bar that turns about a pivot.

Levers act as force multipliers: since

M = F d

, increasing the distance from the pivot means a smaller force can produce the same turning effect.

This is why a long spanner loosens a stiff nut more easily than a short one, and why a long crowbar can lift heavy loads.