Physics

6.8 - Moments - Seesaws & Gears

7 min

How levers work

Lever calculation

How gears work

note 1 of 4

The principle of moments

When an object is balanced about a pivot, it doesn't turn.
The turning effect of a force is its moment:

$M = F d$

where $d$ is the perpendicular distance from the pivot to the line of action of the force.

The principle of moments: for a balanced object, the total clockwise moment equals the total anticlockwise moment.

note 2 of 4

Worked example - Balancing a seesaw

A child of weight 400 N sits 2.0 m from the pivot of a seesaw. A second child of weight 500 N sits on the other side. How far from the pivot must the second child sit for the seesaw to balance?

A seesaw on a triangular pivot with a child at each end, downward arrows labelled 400 N and 500 N, the left distance marked 2.0 m and the right a question mark.

Step 1 - Write down the balance condition

For the seesaw to balance, the total clockwise moment equals the total anticlockwise moment:

$F_{1} d_{1} = F_{2} d_{2}$

Step 2 - Substitution

The first child gives the anticlockwise moment, the second child the clockwise moment:

$400 \times 2.0 = 500 \times d_{2}$

$800 = 500 \times d_{2}$

Step 3 - Solve for the unknown distance

$d_{2} = \frac{800}{500} = 1.6 m$

The heavier child must sit 1.6 m from the pivot - closer than the lighter child, because a larger force needs a shorter distance to give the same moment.

note 3 of 4

How gears work

Gears are toothed wheels that transmit the rotational effect (moment) of a force.
Interlocking gears turn in opposite directions.
A force applied to a larger gear acts further from its pivot, producing a larger moment ( $M = F d$ ).
A larger gear turns slower than a smaller gear it interlocks with.

A small toothed gear meshes with a larger one, a green arrow curving round the small gear labelled faster spin and a pink arrow curving to the large gear labelled slower spin.

note 4 of 4

Gear ratio

The force passed between interlocking gear teeth is the same.
By $M = F d$ , the ratio of the moments equals the ratio of their radii, which equals the ratio of their number of teeth.

Example - A 16-tooth and an 8-tooth gear

Gear ratio is 16 : 8 = 2 : 1.
The 8-tooth gear turns twice for every turn of the 16-tooth gear.
The 16-tooth gear produces double the moment of the 8-tooth gear.

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.

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

GearA toothed wheel that transmits (passes on) the turning effect of a force.

end of notes

Key points to remember

The principle of moments

When an object is balanced about a pivot, it doesn't turn.

The turning effect of a force is its moment:

$M = F d$

where

d

is the perpendicular distance from the pivot to the line of action of the force.

The principle of moments: for a balanced object, the total clockwise moment equals the total anticlockwise moment.

Gear ratio

The force passed between interlocking gear teeth is the same.

M = F d

, the ratio of the moments equals the ratio of their radii, which equals the ratio of their number of teeth.

Example - A 16-tooth and an 8-tooth gear

Gear ratio is 16 : 8 = 2 : 1.

The 8-tooth gear turns twice for every turn of the 16-tooth gear.

The 16-tooth gear produces double the moment of the 8-tooth gear.