Moments, Levers and Gears

📖 In-Depth Theory

Moments

A MOMENT is the turning effect of a force about a pivot.

EQUATION:

Moment = Force × perpendicular distance from the pivot

M = F × d

M = moment (newton-metres, N·m)

F = force (newtons, N)

d = perpendicular distance from line of action of force to pivot (metres, m)

Direction:

CLOCKWISE moment: force tends to turn the object clockwise.

ANTICLOCKWISE moment: force tends to turn the object anticlockwise.

EXAMPLE:

A 50 N force applied 0.4 m from a pivot:

M = 50 × 0.4 = 20 N·m

LARGER MOMENT can be achieved by:

Increasing the FORCE, OR

Increasing the DISTANCE from the pivot.

This is why door handles are at the edge, not the hinge side.

Principle of Moments and Levers

PRINCIPLE OF MOMENTS (equilibrium condition):

For an object in equilibrium, total clockwise moments = total anticlockwise moments about any pivot.

Σ(F × d) clockwise = Σ(F × d) anticlockwise

EXAMPLE — balanced seesaw:

Child A (600 N) sits 1.5 m from pivot.

Clockwise moment = 600 × 1.5 = 900 N·m

Child B must produce 900 N·m anticlockwise.

If Child B weighs 450 N: distance = 900 ÷ 450 = 2 m from pivot.

LEVERS as FORCE MULTIPLIERS:

A lever is a rigid rod that pivots about a fulcrum (pivot).

Small input force × long distance = large output force × short distance.

EXAMPLES: wheelbarrow, crowbar, scissors, tweezers, nutcracker, fishing rod.

Different CLASSES of levers have pivot, effort and load in different positions:

Class 1: pivot between effort and load (seesaw, crowbar).

Class 2: load between pivot and effort (wheelbarrow, nutcracker).

Class 3: effort between pivot and load (tweezers, fishing rod).

Gears

GEARS are toothed wheels that transmit force and rotation.

How gears work:

Meshed gears rotate in OPPOSITE DIRECTIONS.

The teeth interlock — no slipping.

GEAR RATIO:

Gear ratio = number of teeth on driven gear ÷ number of teeth on driving gear

LARGE GEAR driven by SMALL GEAR:

Output gear rotates SLOWER but with MORE FORCE (torque).

Used to increase turning force — e.g. low gear in a car for acceleration.

SMALL GEAR driven by LARGE GEAR:

Output gear rotates FASTER but with LESS FORCE.

Used to increase speed — e.g. high gear in a car at speed.

GEARS AS FORCE MULTIPLIERS:

Like levers, gears convert a small force over a large rotation into a large force over a small rotation (or vice versa).

Energy is conserved — work done is the same (ignoring friction).

APPLICATIONS:

Bicycle gears — change between speed and force.

Car gearbox — match engine output to driving conditions.

Clocks — precise speed reduction from mainspring to hour hand.

Wind turbines — gearbox speeds up slow blade rotation for the generator.

⚠️ Common Mistake

Distance in moments must be the PERPENDICULAR distance from the line of action of the force to the pivot — not the distance along the lever. For the principle of moments, the object must be in equilibrium (balanced and not rotating).

📐 Variables

MMoment (M) is measured in newton-metres (N·m)

FForce (F) is measured in newtons (N)

dPerpendicular distance from pivot (d) is measured in metres (m)

📐 Key Equations

M = F × d

Principle of moments: Σ clockwise moments = Σ anticlockwise moments

📌 Key Note

Moment = F × d (N·m). Principle of moments: clockwise = anticlockwise for equilibrium. Levers: force multipliers — small force × long distance = large force × short distance. Gears: large driven by small = more force, less speed; small driven by large = more speed, less force. Gear ratio = teeth_driven ÷ teeth_driving.

🎯 Matching Activity — Moments and Levers

Match each scenario to the correct moment or principle. — drag the symbols on the right to match the component names on the left.

20 N·m

Drop here

Principle of moments (equilibrium)

Drop here

Force multiplier (lever)

Drop here

Large gear driven by small gear

Drop here

Output rotates slower but with more turning force (torque)

Total clockwise moments = total anticlockwise moments

Small input force × long distance = large output force × short distance

50 N force applied 0.4 m from pivot — M = 50 × 0.4

⚽ FIFA Worked Examples

Moment Calculation

A 300 N person sits 2 m to the right of a seesaw pivot. How far to the left must an 400 N person sit to balance?

F

Principle of moments: clockwise moments = anticlockwise moments → F₁ × d₁ = F₂ × d₂

I

300 × 2 = 400 × d₂

F

600 = 400 × d₂ → d₂ = 600 ÷ 400

A

d₂ = 1.5 m

⭐ Higher Tier Only

Calculate moments and apply the principle of moments to solve equilibrium problems. Solve problems involving multiple forces and pivots. Calculate gear ratios and predict output speed/force. Explain the relationship between gear ratio, speed and force (torque).

🔬 Triple Science Only

Moments, levers and gears (physics only) — not in Combined Science.

🎯 Test Yourself

Question 1 of 2

1. A force of 40 N is applied 0.5 m from a pivot. What is the moment?

2. A bicycle is in a low gear — a small driving gear meshes with a large driven gear. What is the effect?

⭐ How Well Do You Understand This Topic?

Be honest with yourself — this helps you know what to revise!

Don't get it Getting there Nailed it!

🤖 Ask Mr Badmus AI

Stuck? Just ask! 💬

I'll use FIFA for calculations and flag Higher/Triple content clearly.

Moments

Principle of Moments and Levers

Gears

Mr. Badmus AI