PhysicsICSE Class 8 · Force and Pressure

Moment of a Force: Turning Effect, Force × Perpendicular Distance (ICSE Class 8 Physics)

Updated 17 October 2026 · Fact-checked

The moment of a force (its turning effect) about a pivot is the force multiplied by the perpendicular distance of its line of action from the pivot. Its SI unit is the newton metre (N m). A longer distance means a smaller force can give the same moment.

Moment = force × perpendicular distance from the pivot, so doubling the distance lets you halve the force for the same turning effect.

Illustration drawn for QuestionBuddy.

Understand Moment of a Force (Turning Effect)

Turning effect. A force can turn a body about a fixed point called the pivot or fulcrum: a door turns about its hinges, a spanner about the nut, a see-saw about its middle.

Moment of a force.

$moment = F \times d$

where $F$ is the force and $d$ is the perpendicular distance from the pivot to the line of action of the force. SI unit: newton metre (N m).

Factors. The moment is larger when

the force is larger, or
the force acts farther from the pivot.

Zero moment. If the line of action of the force passes through the pivot, $d = 0$ and the moment is zero: pushing a door at its hinge does not turn it.

Direction. A moment is clockwise or anticlockwise. If two forces try to turn a body in opposite directions, the net moment is the difference of the two (the larger decides the direction).

Using a long arm. For the same moment, $F = \frac{moment}{d}$ : a larger $d$ means a smaller force.

door handles are placed far from the hinges;
a long spanner loosens a tight nut more easily than a short one (a pipe slipped over the handle makes it longer still);
tap handles, steering wheels, scissors and wheel-spanners give a large turning effect for a small force.

Distance must be perpendicular. The distance in the formula is measured at right angles to the force, from the pivot. A force pulling along the length of a rod through the pivot gives no turning effect.

Moment of a Force (Turning Effect): formulas and key facts

Moment of a force: $moment = F \times d$; d = perpendicular distance from the pivot; unit N m.
Force for a given moment: $F = \frac{moment}{d}$; Longer arm, smaller force.
Net moment: $net = M_{larger} - M_{smaller}$; Opposite directions subtract.

How to solve Moment of a Force (Turning Effect) questions

Identify the pivot, the force and the perpendicular distance, then multiply.

1Mark the pivot and the line of action of each force.
2Find the perpendicular distance from the pivot to each line; convert cm to m.
3Moment = force × distance, with the unit N m.
4For opposite turning directions, subtract the smaller moment from the larger and name the direction of the larger.
5For "what force", divide the required moment by the arm.

Moment of a Force (Turning Effect) in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Opening a heavy door

Suppose a door is 0.9 m wide with its handle 0.8 m from the hinge, and a push of 5 N at the handle just opens it.

If the same door had to be pushed 0.1 m from the hinge instead, what force would give the same moment?

Try it first, then show the solutionSolution

Moment at the handle $= 5 \times 0.8 = 4$ N m.
$F = \frac{4}{0.1} = 40$ N.

Answer: 40 N, eight times as much.

Memory hook: Push far from the hinge, push less.

Tap and key

Imagine a stiff tap needs a moment of 0.9 N m. A small knob gives an arm of 0.03 m, while a tap key has an effective arm of 0.15 m.

Find the force needed with each.

Try it first, then show the solutionSolution

Knob: $F = \frac{0.9}{0.03} = 30$ N.
Key: $F = \frac{0.9}{0.15} = 6$ N.

Answer: 30 N with the knob and 6 N with the key: five times smaller.

Memory hook: Longer arm, smaller force.

Tricks to remember Moment of a Force (Turning Effect)

Short memory aids. Say each one aloud once, then use it on a question the same day.

F times D
Moment = Force × Distance, always perpendicular.
Use it when: Formula.
Hinge test
Push at the hinge: nothing turns. The farther, the easier.
Use it when: Zero and large moments.
Clock words
Clockwise like a clock hand; anticlockwise is the opposite.
Use it when: Direction.

Moment of a Force (Turning Effect): solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Unit of moment · 1 mark · MCQBoard level

The SI unit of the moment of a force is:
(a) N
(b) N m
(c) N/m
(d) J/s

Try it first, then show the solutionSolution

Moment = force × distance = N × m = N m.

Answer: (b) N m

Example 2: Using a spanner · 2 marks · Short answerBoard level

A force of 40 N is applied at a point 0.25 m from a nut, perpendicular to the spanner. (a) Find the moment. (b) What force at 0.5 m gives the same moment?

Try it first, then show the solutionSolution

(a) $40 \times 0.25 = 10$ N m. (1)
(b) $F = \frac{10}{0.5} = 20$ N. (1)

Answer: (a) 10 N m (b) 20 N

Example 3: A tight nut · 3 marks · Short answerHarder board level

A nut needs a moment of 24 N m to loosen. (a) What force is needed on a spanner of effective length 0.30 m? (b) If a pipe extends the arm to 0.80 m, what force is needed? (c) By what factor does the force fall?

Try it first, then show the solutionSolution

(a) $F = \frac{24}{0.30} = 80$ N. (1)
(b) $F = \frac{24}{0.80} = 30$ N. (1)
(c) $\frac{80}{30} = 2.67$ times (the arm becomes $\frac{0.80}{0.30} = 2.67$ times longer). (1)

Answer: (a) 80 N (b) 30 N (c) about 2.67 times

Example 4: Two forces on a bar · 3 marks · Short answerHarder board level

A bar is pivoted at its centre. A 15 N force acts 0.4 m to the left of the pivot turning it anticlockwise; a 10 N force acts 0.5 m to the right turning it clockwise (both perpendicular to the bar). Find the net moment and its direction.

Try it first, then show the solutionSolution

Anticlockwise moment $= 15 \times 0.4 = 6$ N m. (1)
Clockwise moment $= 10 \times 0.5 = 5$ N m. (1)
Net $= 6 - 5 = 1$ N m, anticlockwise. (1)

Answer: 1 N m anticlockwise

Example 5: Handle position · 4 marks · Case-basedHOTS / competency

A door of width 0.9 m has its handle 0.8 m from the hinge. A student pushes with 5 N at the handle, then with the same force at 0.1 m from the hinge, then at the hinge itself. (a) Find the three moments. (b) Explain why the handle is placed at the edge. (c) Why does a push exactly at the hinge fail?

Try it first, then show the solutionSolution

(a) $5 \times 0.8 = 4$ N m; $5 \times 0.1 = 0.5$ N m; $5 \times 0 = 0$ . (1½)
(b) The farther from the hinge, the larger the moment for the same force, so the door opens easily. (1)
(c) The line of action passes through the pivot, so the perpendicular distance is zero and the moment is zero. (1½)

Answer: (a) 4 N m, 0.5 N m, 0 (b) larger moment (c) distance zero

Where students lose marks in Moment of a Force (Turning Effect)

The slips examiners see most often, and what to write instead.

Mistake: Using the slanted distance
Only the perpendicular distance counts.
Wrong working
"Distance along the rod to the point of push."
Right working
"Perpendicular distance from the pivot to the line of the force."
Do this: Draw the line of action and the right angle.
Mistake: Forgetting to convert cm to m
N m needs metres.
Wrong working
$30 \times 25 = 750$ N m.
Right working
$30 \times 0.25 = 7.5$ N m.
Do this: Convert before multiplying.
Mistake: Adding opposite moments
Clockwise and anticlockwise act against each other.
Wrong working
$6 + 5 = 11$ N m.
Right working
$6 - 5 = 1$ N m anticlockwise.
Do this: Give the direction of the net moment.

Exam tips

Say "perpendicular distance from the pivot" in the definition.
Always give moments in N m, not N or N/m.
Draw a small sketch with pivot, force and distance.
Use clockwise/anticlockwise words when comparing two forces.

Practice questions on Moment of a Force (Turning Effect)

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Very short answerBoard level
Define the moment of a force and name its SI unit.
Hint
Force times distance.
Answer
The moment of a force is the product of the force and the perpendicular distance of its line of action from the pivot; SI unit: newton metre (N m).
Q2 · 3 marks · Short answerHarder board level
Each hand pulls the rim of a steering wheel of diameter 40 cm with a force of 15 N, one pushing up on one side and one pulling down on the other, so both turn the wheel the same way. Find the total moment.
Hint
Radius is half the diameter.
Answer
Radius $= 0.20$ m. Each moment $= 15 \times 0.20 = 3$ N m; total $= 3 + 3 = 6$ N m.
Q3 · 2 marks · Short answerHarder board level
A 30 N force acts on a rod; its line of action passes through the pivot. Find the moment. What would the moment be if the perpendicular distance were 0.2 m?
Hint
Which distance is zero?
Answer
Moment $= 30 \times 0 = 0$ . With a 0.2 m perpendicular distance: $30 \times 0.2 = 6$ N m.
Q4 · 3 marks · Short answerHarder board level
A bolt can be loosened by a moment of 18 N m. A person can apply at most 60 N. What is the shortest spanner arm he can use?
Hint
$d = \frac{moment}{F}$ .
Answer
$d = \frac{18}{60} = 0.30$ m (30 cm).
Q5 · 4 marks · Long answerHOTS / competency
Why do carpenters use a screwdriver with a thick handle for stubborn screws? A screw needs 0.6 N m. Compare the force needed with a handle of effective radius 1.5 cm and 4 cm (hand force at the edge). Which is easier, and by how many times?
Hint
Convert cm to m before dividing.
Answer
$F_{1} = \frac{0.6}{0.015} = 40$ N; $F_{2} = \frac{0.6}{0.04} = 15$ N. The thicker handle needs 15 N, i.e. $\frac{40}{15} \approx 2.67$ times less force: a larger arm gives a larger turning effect.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.SI unit of moment?Show answer
Newton metre (N m).
2.Moment when force passes through the pivot?Show answer
Zero.
3.Why are door handles far from hinges?Show answer
A larger arm gives a larger moment for the same force.
4.Formula for force from moment?Show answer
F = moment ÷ d.
5.Directions of moments?Show answer
Clockwise and anticlockwise.

Moment of a Force (Turning Effect): frequently asked questions

What is the moment of a force?

It is the turning effect of a force about a pivot, equal to the force multiplied by the perpendicular distance of its line of action from the pivot. The SI unit is the newton metre.

Why is it easier to open a door by pushing at the handle than near the hinge?

The handle is far from the hinge, so the perpendicular distance is large and the moment is large for the same force. Near the hinge, the moment is small.

What is the unit of moment of force?

The SI unit is the newton metre (N m), because moment is force in newton times distance in metre.