Turning Effect of ForcesCambridge IGCSE Physics: Revision notes

The moment of a force is a measure of how effectively a force causes something to rotate about a pivot point. It describes the turning effect of a force.

Everyday examples of moments include:

• Opening a door (the handle is far from the hinge pivot, creating a large turning effect)
• Using a spanner to loosen a nut (a longer spanner creates a larger moment with the same force)
• A seesaw or playground lever (children sitting further from the centre create a stronger turning effect)
• Operating a pedal on a bicycle (pushing down creates rotation about the axle)

A moment only exists when a force acts at a distance from a pivot. A force applied directly at the pivot point produces no moment.

The moment of a force is calculated using the equation:

Moment = Force × Perpendicular Distance from Pivot

Or in symbols: M = F × d

Where:

• M = moment (measured in newton-metres, N m)
• F = force applied (measured in newtons, N)
• d = perpendicular distance from the pivot to the line of action of the force (measured in metres, m)

The perpendicular distance is crucial. This is the shortest distance between the pivot and the line along which the force acts. If the force is applied at an angle, only the perpendicular component of this distance counts.

Key points:

• The larger the force, the larger the moment
• The further the force is applied from the pivot, the larger the moment
• Doubling the distance has the same effect as doubling the force (both double the moment)
• Moment is a scalar quantity with direction indicated as clockwise or anticlockwise

The principle of moments states that when an object is in equilibrium (balanced and not rotating), the total clockwise moment about a pivot equals the total anticlockwise moment about the same pivot.

Mathematically: Sum of clockwise moments = Sum of anticlockwise moments

Or: F₁ × d₁ = F₂ × d₂ (for two forces)

This principle applies to any number of forces, provided we:

1. Choose the same pivot point for all calculations
2. Measure all perpendicular distances from that pivot
3. Assign clockwise moments and anticlockwise moments separate totals
4. Set clockwise total equal to anticlockwise total

Applications of the principle:

• Balancing a beam or seesaw: Two children of different weights can balance if placed at appropriate distances from the pivot
• Crane design: Counterweights are positioned far from the pivot to balance heavy loads positioned closer
• Spanner or lever design: The effort force is applied far from the pivot to balance a large load force close to the pivot

An object is in equilibrium when both of the following conditions are met:

1. No resultant force: The sum of all forces acting on the object is zero (or equal and opposite forces act on it)

   • Vertical forces are balanced
   • Horizontal forces are balanced
   • The object does not accelerate in any direction

2. No resultant moment: The sum of all clockwise moments equals the sum of all anticlockwise moments about any pivot

   • The object does not rotate
   • The principle of moments is satisfied

Both conditions must be true simultaneously. An object can have zero resultant force but still rotate if moments are unbalanced, or vice versa.

Examples of objects in equilibrium:

• A book resting on a table (forces and moments balanced)
• A seesaw with both children correctly positioned (moments balanced, both pressing down)
• A suspended mobile with hanging objects (all forces and moments in balance)
• A person standing upright (weight balanced by normal reaction force; moment of weight about the centre of mass is zero)

When there are multiple forces on each side of a pivot, apply the principle of moments by:

1. Calculate the moment of each force separately using M = F × d
2. Sum all clockwise moments (add them together)
3. Sum all anticlockwise moments (add them together)
4. For equilibrium: Set total clockwise moments = total anticlockwise moments

Worked process:

• Identify and label all forces with their magnitudes and perpendicular distances from the chosen pivot
• Calculate each moment
• Assign each moment as clockwise or anticlockwise (use a consistent approach, such as viewing from a fixed direction)
• Add moments in each direction
• If the object is in equilibrium: Sum clockwise = Sum anticlockwise
• If finding an unknown force or distance: use algebra to solve

Common scenarios:

• A plank with loads placed on both sides of a supporting pivot
• A beam balanced on one support with multiple weights distributed along its length
• Levers with effort and load forces, sometimes with resistance forces also present

The principle remains: clockwise moments = anticlockwise moments for equilibrium, regardless of how many forces act.

An experiment to demonstrate equilibrium and the principle of moments typically uses a uniform beam balanced on a pivot (often called a metre rule or lever arm).

Apparatus:

• Uniform beam or metre rule
• Pivot (fulcrum or knife-edge support) placed beneath the beam
• Weights or masses hanging from the beam at known distances from the pivot
• Ruler or measuring tape to determine perpendicular distances

Method:

1. Balance the beam horizontally on the pivot with no weights attached (the beam itself is uniform, so its centre of mass is at the centre)
2. Hang a known weight at a measured distance on one side of the pivot
3. Hang a second known weight at a different distance on the other side
4. Adjust the position of one weight until the beam is balanced horizontally again (equilibrium achieved)
5. Measure the perpendicular distances from the pivot to each weight
6. Record all data

Expected observations:

• When moments are balanced (clockwise = anticlockwise), the beam remains horizontal
• If you calculate moments for each weight, they will be equal
• Changing the weight or distance disrupts equilibrium until moments are rebalanced
• The experiment demonstrates that for equilibrium: F₁ × d₁ = F₂ × d₂

Why this proves the principle: If the beam is horizontal and stationary, there is no resultant moment. Measurement shows that clockwise moments equal anticlockwise moments, confirming the principle of moments as the condition for equilibrium.