Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

1.4.7Motion, Forces and Energy

Moments

5 min read 9 parts Lesson 20 of 36 1 quiz

0%read

Section 1 of 9Turning effects

A force can make an object turn about a fixed point called the pivot (or fulcrum). Opening a door, using a spanner, pushing a see-saw and tightening a bolt all depend on turning effects. The turning effect of a force is called its moment.

The moment depends on two thingsthe size of the force, and how far the line of action of the force is from the pivot.

Section 2 of 9The equation

moment = force × perpendicular distance from the pivot

M = F d

What the symbols mean: moment (N m) · F = force (N) · d = perpendicular distance from the pivot to the line of the force (m)

M is the moment in newton metres (N m), F is the force in newtons (N) and d is the perpendicular distance in metres (m) from the pivot to the line along which the force acts.

The equation
Perpendicular means measured at 90° to the line of the force.
If a force is applied at an angle, the perpendicular distance is smaller than the distance along the object, so the moment is smaller.

The distance must be the shortest (perpendicular) distance from the pivot to the line along which the force acts.

The equation
Imagine extending the force arrow in both directions as a straight line; the moment depends on how far this line passes from the pivot.
If you push a door along its own plane, towards or away from the hinge, the line passes through the hinge and the moment is zero,
  • so the door does not turn.
If you push at 90°, the distance equals the distance from the hinge to the point where you push,
  • and the moment is as large as possible for that force.

Section 3 of 9Direction of a moment

A moment is either clockwise or anticlockwise. A force that would turn the object the way a clock's hands move gives a clockwise moment. When combining moments, treat one direction as positive and the other as negative. Equal clockwise and anticlockwise moments mean no turning, so the object is in rotational balance.

When several forces act, each has its own moment about the chosen pivot. A bar with a 10 N force 0.5 m to the right and a 4 N force 1.0 m to the left of the pivot has a clockwise moment of 5.0 N m and an anticlockwise moment of 4.0 N m, so there is a resultant clockwise moment of 1.0 N m and the bar turns clockwise.

Section 4 of 9Increasing the moment

There are two ways to produce a bigger moment: apply a larger force, or apply the same force further from the pivot.

Increasing the moment
This is why door handles are on the edge furthest from the hinges, why a long spanner loosens a stiff nut and why a long-handled wheelbarrow is easier to lift.
A wheel brace or crowbar is a lever that turns a small force acting over a large distance into a large force at a short distance from the pivot.

A lever is useful because it is a force multiplier. If the effort arm is four times the length of the load arm, then an effort of 50 N can balance a load of 200 N. The energy is not increased: the effort moves four times as far as the load. This is the same idea as a mechanical advantage.

Section 5 of 9Levers and everyday examples

1
A see-saw: a child far from the pivot can balance a heavier child sitting closer.
2
A claw hammer removing a nail: a small force on the long handle gives a large force at the claw.
3
A wheelbarrow, scissors and bottle opener are all levers.
4
A pair of pliers multiplies the force on a small object.

In each case the output force at a short distance is greater than the input force at a large distance, but the output moves a smaller distance.

Section 6 of 9Moments and balance

The idea is developed in the next lessons: the principle of moments states the condition for balance, and the centre of gravity is the point where an object's weight appears to act when working out its moment. Always draw a clear diagram, mark the pivot and measure every distance from the pivot, not from the end of the object.

For practical work, measure distances with a metre rule and forces with newton meters or by hanging known masses (weight = mg). Do experiments with the object at a fixed pivot so that its moment is clearly measured.

Section 7 of 9Worked examples

  1. A force of 25 N acts on a spanner at 0.20 m from the nut. Find the moment.

  2. A nut needs a moment of 60 N m to loosen it. What force is needed on a spanner 0.30 m long, acting at its end at 90°?

  3. A door 0.90 m wide is pushed with a force of 15 N at the handle at 90° to the door. Find the moment about the hinge. Then find the moment if the force is applied 0.45 m from the hinge.

Section 8 of 9Key terms

TermMeaning
MomentTurning effect of a force, force × perpendicular distance, in N m.
PivotFixed point about which an object turns.
LeverRigid bar that turns about a pivot.
ClockwiseTurning direction of the hands of a clock.
Line of actionLine along which a force acts.

Section 9 of 9Exam technique

1
Measuring the distance from the end of the object rather than from the pivot.
2
Using a distance that is not perpendicular to the force.
3
Writing the unit as N/m or J instead of N m.
4
Forgetting that the same force can have different moments about different pivots.
5
Mixing up clockwise and anticlockwise when adding moments.
\n