Turning Effects and Equilibrium

What you'll learn

Turning effects and equilibrium forms a key part of the CIE IGCSE Physics syllabus, examined regularly through calculation and application questions. This topic explores how forces cause objects to rotate, the conditions required for balance, and the principles behind levers, stability and centre of gravity. Understanding these concepts is essential for answering questions worth 4-8 marks in Paper 2 and Paper 4.

Key terms and definitions

Moment of a force — the turning effect of a force about a pivot, calculated as force × perpendicular distance from the pivot (measured in newton-metres, Nm)

Pivot — the fixed point about which an object rotates or turns

Principle of moments — for a system in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point

Centre of gravity — the point at which the entire weight of an object appears to act

Equilibrium — the state of an object when the resultant force is zero AND the resultant moment about any point is zero

Perpendicular distance — the shortest distance from the line of action of a force to the pivot, measured at 90° to the force

Couple — a pair of equal and opposite parallel forces that produce a turning effect without causing linear motion

Stability — the ability of an object to return to its original position after being tilted

Core concepts

Calculating moments

The moment of a force measures its turning effect. Every time a force acts on an object that can rotate, it creates a moment about the pivot point.

The equation for calculating a moment is:

moment = force × perpendicular distance from pivot

M = F × d

Where:

• M is measured in newton-metres (Nm)
• F is measured in newtons (N)
• d is the perpendicular distance measured in metres (m)

Key points for calculations:

• Always measure distance perpendicular to the line of action of the force
• The distance must be from the pivot to where the force acts
• Convert all distances to metres before calculating
• A larger force or a greater distance both increase the moment
• Moments can be clockwise or anticlockwise

Exam tip: When forces act at an angle, you must use only the perpendicular distance. If given a slanted distance, calculate the perpendicular component using trigonometry or resolve the force into components.

The principle of moments and equilibrium

For an object to be in equilibrium, two conditions must be satisfied:

1. The resultant force in any direction must be zero (no linear acceleration)
2. The resultant moment about any point must be zero (no rotational acceleration)

The principle of moments states:

When a body is in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.

Sum of clockwise moments = Sum of anticlockwise moments

This principle applies to:

• Balanced seesaws and beams
• Levers and tools
• Suspended objects
• Structures in static equilibrium

Problem-solving strategy:

1. Identify the pivot point (if not given, choose a convenient point — often where an unknown force acts)
2. Mark all forces acting on the system
3. Measure perpendicular distances from the pivot to each force
4. Calculate clockwise moments (sum them)
5. Calculate anticlockwise moments (sum them)
6. Apply the principle: clockwise moments = anticlockwise moments
7. Solve for the unknown

Levers and mechanical advantage

A lever is a simple machine that uses the principle of moments to multiply force. Levers consist of:

• A rigid bar that can rotate
• A pivot (also called a fulcrum)
• An effort force (the force applied by the user)
• A load force (the resistance or weight being moved)

The mechanical advantage of a lever is given by:

Mechanical advantage = load / effort

For a lever in equilibrium:

• Effort × distance from pivot to effort = Load × distance from pivot to load

This means a small effort force can move a large load when the effort acts further from the pivot than the load.

Common examples tested in CIE IGCSE papers:

• Wheelbarrow: load between pivot (wheel) and effort — mechanical advantage > 1
• Scissors: pivot at one end, effort and load on blade — mechanical advantage varies with cutting position
• Crowbar: pivot near load, effort at far end — large mechanical advantage
• Spanner: increases perpendicular distance from nut (pivot), increasing moment for same effort

Centre of gravity and stability

The centre of gravity is the single point where all the weight of an object can be considered to act. For regular, uniform objects:

• Rectangular lamina: at the geometric centre
• Sphere: at the centre
• Uniform rod: at the midpoint

For irregular objects, the centre of gravity is found experimentally by:

1. Suspending the object freely from one point
2. Drawing a vertical line downward from the suspension point (using a plumb line)
3. Suspending from a different point
4. Drawing another vertical line
5. The intersection of the lines is the centre of gravity

Stability depends on three factors:

1. Base area: wider base = more stable
2. Height of centre of gravity: lower centre of gravity = more stable
3. Position of centre of gravity: stability is greatest when the centre of gravity is directly above the base

An object will topple when a vertical line drawn through its centre of gravity falls outside its base. This occurs when the object is tilted beyond a critical angle.

Applications tested in exams:

• Racing cars: wide wheelbase, low centre of gravity for stability at high speeds
• Double-decker buses: heavy ballast at bottom to lower centre of gravity
• Tall vehicles: prone to toppling on sharp turns or slopes
• Stacking objects: wider, heavier items at bottom for stability

Couples and their effects

A couple consists of two equal, parallel forces acting in opposite directions, separated by a perpendicular distance. Unlike a single force, a couple produces:

• Pure rotation (no linear motion)
• A turning effect regardless of the pivot position

Moment of a couple = one of the forces × perpendicular distance between the forces

Examples include:

• Turning a steering wheel (hands push in opposite directions)
• Using a screwdriver (fingers apply opposite forces on the handle)
• Opening a tap (thumb and finger exert opposite forces)
• Winding a clock with a key

The moment of a couple is the same about any point, which distinguishes it from the moment of a single force.

Worked examples

Example 1: Uniform beam in equilibrium

Question: A uniform beam of length 4.0 m and weight 50 N is supported at its centre. A child of weight 300 N sits 1.2 m from the left end. How far from the right end must a second child of weight 400 N sit to balance the beam?

Solution:

Choose the pivot at the centre of the beam (2.0 m from each end).

Weight of beam acts at centre (pivot), so contributes zero moment.

First child sits 1.2 m from left end = 2.0 - 1.2 = 0.8 m left of centre

Clockwise moment = 300 N × 0.8 m = 240 Nm

For equilibrium: anticlockwise moment = clockwise moment

Let second child sit distance x from right end = (2.0 - x) from centre (on right side)

Anticlockwise moment = 400 N × (2.0 - x) m

400(2.0 - x) = 240

800 - 400x = 240

400x = 560

x = 1.4 m

Answer: 1.4 m from the right end [3 marks]

Example 2: Lever system

Question: A gardener uses a spade as a lever to lift a rock. She applies a downward force of 150 N at a point 1.2 m from the pivot. The rock is 0.15 m from the pivot. Calculate: (a) The moment produced by the gardener [2] (b) The maximum weight of rock that can be lifted [2]

Solution:

(a) Moment = force × perpendicular distance Moment = 150 N × 1.2 m Moment = 180 Nm [2 marks]

(b) For equilibrium, clockwise moments = anticlockwise moments

Moment from rock = moment from effort

Weight of rock × 0.15 m = 180 Nm

Weight of rock = 180 / 0.15

Weight of rock = 1200 N [2 marks]

Example 3: Stability problem

Question: Explain why a loaded truck is less likely to topple over when: (a) The load is placed low down rather than high up [2] (b) The truck has a wide wheelbase [2]

Solution:

(a) Placing the load low down lowers the position of the centre of gravity [1]. When the centre of gravity is lower, the truck must be tilted through a larger angle before the vertical line through the centre of gravity falls outside the base / wheel positions [1].

(b) A wide wheelbase increases the area of the base [1]. The vertical line through the centre of gravity can move further sideways before falling outside the base, so the truck can tilt more before toppling [1].

Common mistakes and how to avoid them

• Mistake: Using the wrong distance in moment calculations (e.g., measuring along a slanted beam instead of perpendicular distance). Correction: Always measure the perpendicular (shortest) distance from the pivot to the line of action of the force, at 90° to the force direction.

• Mistake: Forgetting to convert centimetres to metres before calculating moments, giving answers 100 times too large. Correction: Check units carefully — if force is in N and distance in cm, convert cm to m by dividing by 100 before calculating.

• Mistake: Stating that an object in equilibrium has "no forces acting" or "all forces are balanced." Correction: An object in equilibrium has zero resultant force and zero resultant moment, but individual forces do act — they simply cancel out.

• Mistake: Confusing centre of gravity with centre of mass or geometric centre for non-uniform objects. Correction: Centre of gravity is where weight acts; for uniform objects in a uniform gravitational field, this coincides with the geometric centre, but for irregular or non-uniform objects, it must be found experimentally or by calculation.

• Mistake: Assuming the weight of a beam always creates a moment about any pivot. Correction: The weight of a uniform beam only creates a moment if the pivot is NOT at the centre; if the pivot is at the centre of gravity, the moment from the beam's weight is zero.

• Mistake: Calculating moments about different points in the same problem, leading to confusion. Correction: Choose one pivot point and calculate ALL moments about that same point; the pivot point can be chosen strategically to eliminate unknown forces from the calculation.

Exam technique for Turning Effects and Equilibrium

• Command word "Calculate": Show your working clearly: write the formula, substitute values with units, then give the final answer with correct units. Marks are awarded for method even if the final answer is wrong — typically 1 mark for correct formula/method, 1 mark for correct substitution and answer for a 2-mark question.

• Drawing force diagrams: When asked to "show the forces acting," draw arrows from the point of application, label each force clearly (e.g., "Weight 50 N", "Reaction force R"), and ensure arrow lengths are roughly proportional to force magnitudes. Arrows should show the direction of force accurately.

• Extended response on stability: Structure answers logically: first state the relevant factor (base width / centre of gravity position), then explain the effect on stability, finally link to toppling conditions (vertical line through centre of gravity relative to base). This typically earns 2-3 marks per factor.

• Problem-solving with moments: When multiple forces act, make a clear table or list showing each force, its distance from the pivot, and its moment (with direction). This prevents errors and earns method marks even if arithmetic is incorrect. Common questions are worth 4-6 marks total.

Quick revision summary

Moment = force × perpendicular distance (Nm). For equilibrium: sum of clockwise moments equals sum of anticlockwise moments. Levers multiply force using the principle of moments. Centre of gravity is the point where weight acts; stability increases with wider base and lower centre of gravity. An object topples when the vertical line through its centre of gravity falls outside the base. A couple is two equal opposite forces producing pure rotation. Always use perpendicular distances and convert units to metres.