Moments

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Notes

Moments

A **moment** is the turning effect of a force about a pivot.
Examples: see-saw, spanner, door, crane, screwdriver, tap, wheelbarrow, scissors.
Rotation can be **clockwise** or **anticlockwise** (use clock hands as reference).
Equation: **moment = force × perpendicular distance from pivot** (M = F × d).
Units: **newton metre (N m)** or **newton centimetre (N cm)**.
Increasing distance from pivot reduces the force needed for the same moment.

Principle of Moments (Core)

**Principle of moments**: For a balanced object, total clockwise moment equals total anticlockwise moment.
Clockwise moment = anticlockwise moment.
Used to solve for unknown forces or distances when the system is in equilibrium.
Always convert distances to metres unless question specifies N cm.

Principle of Moments (Extended)

Extended tier: multiple forces on each side of the pivot.
Sum of clockwise moments = sum of anticlockwise moments.
Example: F2 × d2 = (F1 × d1) + (F3 × d3).
Ensure all distances are in the same units and directions are correctly identified.

Equilibrium

**Equilibrium** means a state of balance or stability – no resultant force and no resultant moment.
Conditions: (1) forces balanced (resultant force = 0), (2) clockwise moments = anticlockwise moments (resultant moment = 0).
If either condition fails, the object will accelerate or rotate.

Centre of Gravity

**Centre of gravity** is the point through which the weight of an object acts.
For symmetrical objects of uniform density, it lies at the centre of symmetry.
The centre of gravity can lie inside or outside the object.
In force diagrams, always draw weight from the centre of gravity.

Stability

An object is **stable** when its centre of gravity lies above its base.
If the line of action of weight falls outside the base, the object **topples**.
Stability increases with a **low centre of gravity** and a **wide base**.
Tall, narrow objects (e.g., buses) are less stable and topple more easily.

Investigating Centre of Gravity (Suspension Method)

Aim: find the centre of gravity of an irregularly shaped plane lamina.
Method: punch 3 holes near edges, hang lamina from a clamp, use a plumb line to mark vertical line of weight.
Repeat for each hole – the intersection of the three lines is the centre of gravity.
When suspended, the object settles with its centre of gravity directly below the point of suspension.
Avoid parallax error by viewing plumb line straight on; allow lamina to settle before marking.

Demonstrating Equilibrium (Extended Experiment)

Aim: show no resultant moment for an object in equilibrium.
Use a metre ruler pivoted at its centre, hang unequal masses on cotton loops at different distances.
Adjust distances until ruler is horizontal and balanced.
Calculate anticlockwise moment (m1 × g × d1) and clockwise moment (m2 × g × d2).
Results should show anticlockwise moment = clockwise moment for equilibrium.
Control variables: equal cotton loop lengths, no friction at pivot.

Diagram showing the turning effect of a force: a spanner turning a bolt. The moment depends on force and perpendicular distance from pivot.

Principle of moments: clockwise moment equals anticlockwise moment for a balanced beam.

Practice questions

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1.What is the moment of a force?
Easy
- AThe turning effect of a force about a pivot
- BThe speed at which a force is applied
- CThe energy transferred by a force
- DThe power output of a force
2.Which of the following is an example of the turning effect of a force?
Easy
- AA child sitting on a see-saw
- BA book resting on a table
- CA ball rolling down a hill
- DA magnet attracting a nail
3.What is the unit of a moment?
Easy
- Anewton metre (N m)
- Bnewton (N)
- Cmetre (m)
- Djoule (J)
4.A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. What is the moment?
Easy
- A5 N m
- B20 N m
- C0.5 N m
- D10.5 N m
5.A uniform metre rule is balanced at its midpoint. A 2.0 N weight is placed 30 cm from the pivot on the left. Where must a 3.0 N weight be placed on the right to balance the rule?
Medium
- A20 cm from the pivot
- B30 cm from the pivot
- C45 cm from the pivot
- D15 cm from the pivot
6.The principle of moments states that for an object in equilibrium:
Medium
- Atotal clockwise moment = total anticlockwise moment
- Btotal clockwise moment > total anticlockwise moment
- Ctotal clockwise moment < total anticlockwise moment
- Dthe sum of forces is zero
7.An object will topple over when:
Medium
- Aits centre of gravity lies outside its base
- Bits centre of gravity is directly above its base
- Cits base is very wide
- Dits centre of gravity is low
8.Which of the following increases the stability of an object?
Medium
- ALowering its centre of gravity
- BRaising its centre of gravity
- CMaking its base narrower
- DMaking it taller

More questions

9.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin. It comes to rest with its centre of gravity:
Hard
- Adirectly below the point of suspension
- Bdirectly above the point of suspension
- Cat the point of suspension
- Dat the geometric centre of the lamina
10.A man uses a spanner to turn a nut. He applies a force of 40 N at a distance of 0.25 m from the pivot. What is the moment?
Hard
- A10 N m
- B160 N m
- C0.25 N m
- D40.25 N m
11.A beam is in equilibrium with three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). What is the magnitude of F3?
Hard
- A25 N
- B35 N
- C5 N
- D45 N
12.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. If the counterweight is 5000 N, what is the maximum load that can be lifted without toppling?
Hard
- A10000 N
- B2500 N
- C5000 N
- D2000 N
13.A uniform metre rule is balanced horizontally on a pivot at its centre. A 4.0 N weight is placed 20 cm from the pivot on the left side. A 2.0 N weight is placed 30 cm from the pivot on the right side. What is the resultant moment about the pivot?
Medium
- A0.2 N m clockwise
- B0.2 N m anticlockwise
- C1.4 N m clockwise
- D1.4 N m anticlockwise
14.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin through a hole near its edge. It comes to rest. Where is its centre of gravity relative to the point of suspension?
Medium
- Adirectly below the point of suspension
- Bdirectly above the point of suspension
- Cat the same height as the point of suspension
- Dat the centre of the lamina
15.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the student repeats the process with two more holes. The three lines intersect at a point. What does this point represent?
Hard
- Athe centre of gravity of the lamina
- Bthe point of suspension
- Cthe centre of mass of the lamina
- Dthe centre of the lamina
16.In the experiment to demonstrate equilibrium using a metre ruler and masses, which of the following is a control variable?
Medium
- Athe length of the cotton loops on each side of the pivot
- Bthe mass added to the hangers
- Cthe distance of the masses from the pivot
- Dthe moment calculated
17.In the equilibrium experiment using a metre ruler, the ruler is balanced on a pin. One student suggests that friction between the ruler and the pin might affect the results. Which of the following is the best way to reduce this systematic error?
Hard
- Aensure the ruler is perfectly horizontal before adding masses
- Buse a spirit level to check the ruler's angle
- Ccheck that the ruler is free to rotate with no friction
- Duse a G clamp to secure the clamp stand
18.Which of the following is the correct definition of the centre of gravity of an object?
Easy
- Athe point through which the weight of the object acts
- Bthe point at which the object is balanced
- Cthe geometric centre of the object
- Dthe point where the object's mass is concentrated
19.A uniform metre rule is balanced on a pivot at its centre. A 2.0 N weight is placed at the 20 cm mark on the left side. Where should a 3.0 N weight be placed on the right side to balance the rule?
Medium
- A20 cm
- B30 cm
- C40 cm
- D50 cm
20.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight has a weight of 5000 N. What is the maximum load that can be lifted without the truck toppling?
Hard
- A2500 N
- B5000 N
- C10000 N
- D20000 N
21.Which of the following is a unit of moment?
Easy
- Anewton metre
- Bnewton per metre
- Cjoule
- Dwatt
22.In the experiment to find the centre of gravity of an irregular lamina, why is it important to punch the holes before drawing the lines?
Hard
- Ato ensure the holes are at the correct positions
- Bbecause punching holes after can affect the position of the centre of gravity
- Cto make the lamina easier to hang
- Dto avoid parallax error
23.An object will topple over when its centre of gravity:
Easy
- Alies above its base
- Blies outside its base
- Cis at its lowest possible point
- Dis directly above the pivot
24.The centre of gravity of an object is defined as:
Easy
- Athe point through which the weight of the object acts
- Bthe geometric centre of the object
- Cthe point where all the mass is concentrated
- Dthe point where the object balances when suspended
25.A uniform metre rule is balanced at its centre. Where is its centre of gravity?
Easy
- AAt the 50 cm mark
- BAt the 0 cm mark
- CAt the 100 cm mark
- DAt the point of suspension
26.A force of 5 N is applied at a perpendicular distance of 20 cm from a pivot. What is the moment in N m?
Medium
- A1.0 N m
- B100 N m
- C0.25 N m
- D25 N m
27.Which of the following describes a system in equilibrium?
Medium
- AThe sum of clockwise moments equals the sum of anticlockwise moments
- BThe forces are balanced but there is a resultant moment
- CThe object is moving at constant velocity
- DThe object is accelerating
28.A uniform beam is balanced on a pivot. A 10 N weight is placed 0.4 m to the left of the pivot. Where must a 5 N weight be placed on the right to balance the beam?
Medium
- A0.8 m from the pivot
- B0.2 m from the pivot
- C0.4 m from the pivot
- D0.6 m from the pivot
29.An object is more stable when its centre of gravity is:
Medium
- Alow and its base is wide
- Bhigh and its base is narrow
- Clow and its base is narrow
- Dhigh and its base is wide
30.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a hole near its edge. It comes to rest. Where is its centre of gravity?
Hard
- ADirectly below the point of suspension
- BDirectly above the point of suspension
- CAt the point of suspension
- DAt the geometric centre of the lamina
31.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action, what should the student do next?
Hard
- ASuspend the lamina from a different hole and draw another line
- BWeigh the lamina and calculate the centre of gravity
- CMeasure the distance from the hole to the line
- DCut the lamina along the line
32.A beam is acted upon by three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). The beam is in equilibrium. What is the magnitude of F3?
Hard
- A25 N
- B5 N
- C15 N
- D10 N
33.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight is 5000 N. The truck is in equilibrium. What is the load?
Hard
- A10,000 N
- B2500 N
- C5000 N
- D2000 N
34.A uniform metre rule is pivoted at its centre. A 2.0 N weight is placed at the 20 cm mark on the left side. A 3.0 N weight is placed at the 70 cm mark on the right side. What is the resultant moment about the pivot?
Medium
- A0.2 N m clockwise
- B0.2 N m anticlockwise
- C0.4 N m clockwise
- D0.4 N m anticlockwise
35.In the experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin through a hole near its edge. It comes to rest. Where is its centre of gravity located?
Medium
- ADirectly below the point of suspension
- BDirectly above the point of suspension
- CAt the point of suspension
- DAt the geometric centre of the lamina
36.A beam is in equilibrium with three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot. What is the magnitude and direction of F3?
Hard
- A5 N anticlockwise
- B5 N clockwise
- C20 N anticlockwise
- D20 N clockwise
37.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight is 5000 N. What is the maximum load that can be lifted without the truck toppling?
Medium
- A10000 N
- B2500 N
- C2000 N
- D5000 N
38.In an experiment to demonstrate equilibrium, a metre ruler is balanced on a pivot at its centre. A 100 g mass is hung at the 20 cm mark on the left, and a 200 g mass is hung at the 70 cm mark on the right. What is the resultant moment about the pivot? (Take g = 10 N/kg)
Hard
- A0.1 N m clockwise
- B0.1 N m anticlockwise
- C0.3 N m clockwise
- D0.3 N m anticlockwise
39.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the process is repeated from two other holes. Why are three lines drawn?
Medium
- ATo ensure accuracy by finding the intersection point
- BTo measure the weight of the lamina
- CTo check if the lamina is uniform
- DTo determine the area of the lamina
40.A uniform beam of weight 120 N and length 6.0 m is supported at its ends. A load of 80 N is placed 2.0 m from the left end. What is the upward force at the left support?
Hard
- A80 N
- B100 N
- C60 N
- D120 N

Slides

What is a Moment?

A moment is the turning effect of a force about a pivot.
Examples: a child on a seesaw, turning a spanner, opening a door.
Forces can cause rotation clockwise or anticlockwise about a pivot.

What is the moment of a force?

The size of the force
The turning effect of a force about a pivot
The distance from the pivot
The weight of an object

The Moment Equation

Moment = force × perpendicular distance from pivot.
Force must be perpendicular to the distance from the pivot.
Unit: newton metre (N m) or newton centimetre (N cm).

Moment = ____ × perpendicular distance from pivot.

Clockwise and Anticlockwise Moments

A force can cause rotation clockwise or anticlockwise about a pivot.
Use the hands of a clock to decide the direction.
The direction matters when applying the principle of moments.

A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. What is the moment?

5 N m
20 N m
0.5 N m
10 N m

Principle of Moments

For an object in equilibrium, total clockwise moment = total anticlockwise moment.
This is called the principle of moments.
It allows us to calculate unknown forces or distances.

Which of these are true for an object in equilibrium?

The forces on the object are balanced.
There is a resultant moment.
Total clockwise moment equals total anticlockwise moment.
The object must be stationary.

Worked Example: Seesaw

A parent (690 N) sits 0.3 m from the pivot on one side.
A child (140 N) sits on the other side.
Using the principle of moments, find the child's distance from the pivot.

Using the principle of moments: 690 N × 0.3 m = 140 N × ____. So distance = ____ m.

Equilibrium

Equilibrium means a state of balance or stability.
Conditions: no resultant force and no resultant moment.
The sum of clockwise moments equals sum of anticlockwise moments.

Which condition is NOT required for an object to be in equilibrium?

Forces are balanced
No resultant moment
Object is at rest
Clockwise moment = anticlockwise moment

Centre of Gravity

The centre of gravity is the point through which the weight of an object acts.
For a symmetrical object of uniform density, it is at the centre.
The position of the centre of gravity affects stability.

Where is the centre of gravity of a uniform sphere?

At the top
At the centre
At the bottom
Outside the sphere

Stability

An object is stable if its centre of gravity lies above its base.
If the centre of gravity is no longer over the base, the object topples.
Wider base and lower centre of gravity increase stability.

Which factors increase stability?

Wider base
Higher centre of gravity
Lower centre of gravity
Narrower base

Finding Centre of Gravity Experimentally

For an irregular shape, use the suspension method.
Hang the shape from a point; it settles with CG directly below the point of suspension.
Draw a vertical line from the suspension point; repeat from two other points; the lines intersect at the CG.

When an object is suspended, its centre of gravity lies directly ____ the point of suspension.

How many suspension points are typically used to find the centre of gravity of an irregular lamina?

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