Moments — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

Section 1 of 23Moment of a force

Definition

• Definition the moment of a force is its turning effect about a pivot.
• A force can make an object rotate clockwise or anticlockwise about a fixed pivot.

Everyday examples

• Everyday examples a child on a see-saw, turning a spanner, opening a door, a crane lifting supplies, a screwdriver opening a paint tin, a tap, a wheelbarrow and scissors.

Deciding the direction

• Deciding the direction imagine only that force acting on the object about the pivot.
• If the object turns like the hands of a clock the moment is clockwise.

Section 2 of 23The moment equation

Equation

• Equation moment = force × perpendicular distance from the pivot, or M = Fd.
• The distance must be measured at right angles to the line of the force.
• On a horizontal beam the forces that cause moments are the ones acting up or down.

Units

• Units newton metres (N m), or N cm if the distance is in centimetres.
• Convert distances to metres unless told otherwise.
• Avoid N/m, which suggests division, and joules, which are never accepted for a moment.

Section 3 of 23Why distance matters

Why distance matters

Greater distance, smaller force

• Greater distance, smaller force a larger distance from the pivot needs less force for the same moment.

Door example

• Door example pushing next to the hinge needs a large force, while pushing at the handle needs much less.

Spanner example

• Spanner example a longer spanner makes a stiff bolt easier to turn.

Section 4 of 23Principle of moments (core)

Statement

• Statement for a balanced object the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.

Core use

• Core use one force on each side of the pivot, so F₁d₁ = F₂d₂.

Section 5 of 23Principle of moments (extended)

Several forces

• Several forces add all the moments on each side separately.
• Sum of clockwise moments = sum of anticlockwise moments.
• For example F₂d₂ = F₁d₁ + F₃d₃.

Weight of the beam

• Weight of the beam a beam pivoted at its centre contributes no moment because its distance from the pivot is zero.
• If the pivot is off-centre, the beam's own weight must be included.

Section 6 of 23Method for balance problems

1

Draw the beam, the pivot and every force with its distance.

2

Label each moment clockwise or anticlockwise.

3

Convert all distances to the same unit, preferably metres.

4

Write the principle: total clockwise = total anticlockwise.

5

Substitute Fd for each force and solve for the unknown.

6

Check the answer is sensible, for example the lighter person sits further out.

Section 7 of 23Moments in everyday devices

Lever

• Lever a long handle gives a large moment from a small effort.

Wheelbarrow

• Wheelbarrow the load is close to the wheel pivot, so a small lifting force at the handles balances it.

Crane

• Crane a counterweight on the short arm balances the load on the long arm.

Door

• Door the handle is placed far from the hinges to give a large moment.

Section 8 of 23More from the specification

More from the specification

Static equilibrium in structural loops

• Static equilibrium in structural loops equating clockwise and anticlockwise turning moments prevents rotation and ensures static stability throughout closed structural loops.

Principle of Moments and Equilibrium

• An object is in rotational equilibrium when there is no resultant turning effect,
• meaning total clockwise moments equal total anticlockwise moments about any 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)

Locating Center of Gravity of a Plane Lamina

• In a laboratory experiment, an irregular plane lamina is suspended from a clamp;
  • vertical lines drawn using a plumb line intersect to locate its center of gravity.

Balancing Masses on a Meter Ruler

• Suspending calibrated masses at various distances along a balanced meter ruler demonstrates how varying force and perpendicular distance maintains equilibrium.

Center of Gravity Position and Stability

• Lowering the position of the center of gravity and broadening the base of an object increases physical stability against toppling.

Gravity

• A force of attraction between objects with mass.

Lamina

• A thin flat sheet.

Equilibrium

• State with zero net force.

Position

• Location relative to a reference point.

Resultant

• Vector sum of two or more vectors.

Topple

• Tip over because the weight acts outside the base.

Section 9 of 23Several forces on a beam

Extended principle

• Extended principle sum of clockwise moments = sum of anticlockwise moments.
• For forces F₁ and F₃ anticlockwise and F₂ clockwise: F₂d₂ = F₁d₁ + F₃d₃.

Beam weight

• Beam weight a uniform beam pivoted at its centre contributes no moment because its weight acts through the pivot.
• If the pivot is elsewhere, the beam's weight acts at its centre and gives a moment.

Direction of each moment

• Direction of each moment decide it by imagining that force alone turning the beam.

Section 10 of 23Conditions for equilibrium

Definition

• Definition an object is in equilibrium when there is no resultant force and no resultant moment.

Two conditions

• Two conditions both must be satisfied.
• The forces are balanced, so there is no resultant force.
• The clockwise moments equal the anticlockwise moments, so there is no resultant moment.

Common error

• Common error stating only that the forces are balanced and forgetting the moments.

Section 11 of 23Equipment for demonstrating equilibrium

Equipment	Purpose
Metre ruler with a hole at the centre	Forms the beam
Optical pin and cork, clamp stand	Act as the pivot
Two 100 g hangers and eight 100 g masses	Provide the forces
Cotton loops	Attach the hangers to the ruler
Modelling clay	Makes the unloaded ruler balance horizontally

Section 12 of 23Method

1

Secure the pin in the clamp stand and mount the ruler on it so that it sits horizontal.

2

Hang unequal loads on each side while a second person steadies the beam.

3

Adjust the distances of the masses until the beam balances horizontally.

4

Record each mass and its distance from the pivot.

5

Repeat with different loads.

Variables

• Variables mass and distance are the independent variables, and the moment is the dependent variable.

Control

• Control the loops must have equal lengths and the pivot must stay at the ruler's centre.

Section 13 of 23Analysis, errors and safety

Analysis, errors and safety

Calculations

• F = mg and M = Fd for each side, with grams converted to kilograms and cm to metres.
• The results should show the anticlockwise moment equals the clockwise moment, so there is no resultant moment.

Systematic errors

• Systematic errors view the loops straight on to avoid parallax, check the loops have equal length and ensure the pin has no friction.

Random errors

• Random errors work away from draughts, use a spirit level to confirm the beam is horizontal and repeat to take a mean.

Assumptions

• Assumptions the cotton has negligible mass and each mass plus hanger is 100 g, which can be checked on a balance.

Safety

• Safety wear goggles, clamp the stand with a G clamp, stand while working and place a soft mat below the masses.

Section 14 of 23More from the specification

More from the specification

Moment of a force definition

• The moment of a force is a measure of its turning effect about a pivot, calculated as moment = force * perpendicular distance to the line of action.

Principle of moments for equilibrium

• For an object in rotational equilibrium, the sum of clockwise moments about any pivot must equal the sum of anticlockwise moments.

Centre of gravity and stability

• The centre of gravity is the single point where the total weight of a body may be considered to act;
  • low centres of gravity and wide base areas maximize stability.

Turning effect

• Moment that rotates the coil.

Gravity

• A force of attraction between objects with mass.

Lamina

• A thin flat sheet.

Position

• Location relative to a reference point.

Topple

• Tip over because the weight acts outside the base.

Perpendicular

• At right angles.

Section 15 of 23What the centre of gravity is

Definition

• Definition the centre of gravity is the point through which the weight of an object acts.

Regular objects

• Regular objects a symmetrical object of uniform density has its centre of gravity at its point of symmetry.
• A sphere has its centre of gravity at its centre.

Hypothetical point

• Hypothetical point it can lie inside or outside the body.
• It moves when the shape changes, so a person leaning forward has a lower centre of gravity.

Force diagrams

• Force diagrams always draw the weight force from the centre of gravity.

Section 16 of 23Stability

Stable object

• Stable object its centre of gravity lies above its base.

Toppling

• Toppling if the line of action of the weight falls outside the base, a resultant moment turns the object over.

More stable designs

• More stable designs a low centre of gravity and a wide base.
• Cars, high chairs and Bunsen burners have wide bases.

Less stable designs

• Less stable designs tall objects on a narrow base topple easily.
• Bowling pins are designed to topple and lorries are advised to avoid exposed bridges in high wind.

Section 17 of 23Comparing stable and unstable objects

Feature	More stable	Less stable
Centre of gravity	Low	High
Base	Wide	Narrow
Tilt before toppling	Large angle	Small angle
Example	Racing car	Bus (topples at about 45°; a car tilts to about 60°)

Section 18 of 23Finding the centre of gravity of a lamina

1

Punch three holes near the edge of the lamina in different places.

2

Hang a cork horizontally in a clamp and hang the lamina from a pin through one hole.

3

Check that the lamina swings freely and let it settle.

4

Hang a plumb line from the same pin and mark where it passes over the lamina.

5

Repeat with the other holes to draw three lines.

6

The centre of gravity is where the lines cross.

7

Check by balancing the lamina on a pin tip at that point.

Section 19 of 23Why the method works and its errors

Why the method works and its errors

Principle

• Principle a hanging object settles with its centre of gravity directly below the pivot, so the plumb line passes through it.
• Two lines are enough to locate the point, and the third checks the first two.

Systematic errors

• Systematic errors view the plumb line straight on, use a sharp pencil and mark dots then rule the lines after removing the lamina.

Random errors

• Random errors allow the lamina to settle and punch the holes before the investigation, since later holes change the centre of gravity.

Safety

• Safety secure the clamp stand and push the sharp pin into a cork when not in use.

Section 20 of 23More about centre of gravity

Weight arrow

• Weight arrow it starts at the centre of gravity and points straight down.

Symmetry rule

• Symmetry rule a uniform rectangle has its centre of gravity where its diagonals cross.

Tilting

• Tilting an object tilted until its centre of gravity is above the edge of the base is on the point of toppling.

Lowering it

• Lowering it adding weight at the bottom lowers the centre of gravity and makes an object more stable.

Section 21 of 23More from the specification

1Rotational moment balancing loops

• Rotational moment balancing loops evaluating clockwise and anticlockwise moments about pivots confirms mechanical equilibrium in articulated structural loops.

2Definition of the Moment of a Force

• The moment of a force measures its turning effect about a fixed pivot, calculated as the force multiplied by the perpendicular distance from the line of action of the force to the pivot: Moment = F * d.
  • (measured in N m)

3Principle of Moments for Rotational Equilibrium

• When an object is in rotational equilibrium, the total sum of clockwise moments about any pivot must equal the total sum of anticlockwise moments.
  • (such as a balanced meter ruler or a see-saw with an adult and child)

4Laboratory Balancing Experiment

• In an experiment using a uniform metre ruler suspended horizontally from a clamp, known weights are hung at varying positions until balance is achieved, confirming that F1 * d1 = F2 * d2.

5Conditions for Complete Static Equilibrium

• For a planar rigid body to remain in complete equilibrium, the net external forces in all directions must be zero and the net turning moments about any point must be zero.
  • (translational equilibrium)

6Principle of moments equilibrium

• Principle of moments equilibrium for a balanced beam in rotational equilibrium, total clockwise moments equal total anticlockwise moments about the pivot.

7Moment calculation

• Moment calculation moment equals applied perpendicular force multiplied by perpendicular distance from the pivot to the line of action.

8Balancing experimental beam

• Balancing experimental beam adjusting the position of a known mass on a graduated metre ruler verifies equilibrium conditions.

9Turning effect

• Moment that rotates the coil.

10M = Fd

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

11Clockwise

• Turning in the direction of a clock's hands.

12Anticlockwise

• Turning against the direction of a clock's hands.

13Distance

• Total length of path travelled, a scalar.

14Equilibrium

• State with zero net force.

15Position

• Location relative to a reference point.

16Perpendicular

• At right angles.

Section 22 of 23Key terms

Term	Meaning
Moment	The turning effect of a force about a pivot, force × perpendicular distance.
Pivot	The fixed point about which an object turns.
Principle of moments	For a balanced object, total clockwise moment equals total anticlockwise moment.
Clockwise	Turning in the direction of a clock's hands.
Anticlockwise	Turning against the direction of a clock's hands.
Newton metre	The unit of moment.

Term	Meaning
Equilibrium	No resultant force and no resultant moment.
Resultant moment	The net turning effect after clockwise and anticlockwise moments are combined.
Pivot	The point about which a beam can turn.
Parallax error	An error from viewing a scale at an angle.
Uniform beam	A beam whose weight acts at its centre.

Term	Meaning
Centre of gravity	The point through which the weight of an object acts.
Stability	The tendency of an object to stay upright without toppling.
Plumb line	A thread with a weight that hangs vertically.
Lamina	A thin flat sheet.
Line of action	The line along which a force acts.

Section 23 of 23Exam technique

1

Measuring the distance along the force instead of perpendicular to it.

2

Leaving distances in centimetres in one moment and metres in another.

3

Stating the principle as "the moments are equal" with no clockwise or anticlockwise.

4

Giving the unit of a moment as N/m or J — use N m.

1

Stating only that forces are balanced when asked for the conditions for equilibrium.

2

Using the distance from the end of the beam instead of from the pivot.

3

Adding the weight of a uniform beam as a moment when the pivot is at its centre.

4

Leaving masses in grams in M = mgd.

1

Saying the centre of gravity must be inside the object.

2

Confusing stability with weight — it depends on the base and the height of the centre of gravity.

3

Punching extra holes in the lamina after finding the point.

4

Using only one suspension line.