Moments, Levers and Gears [H]

This lesson covers moments, levers, and gears as required by the AQA GCSE Physics specification (4.5.5). This is Higher Tier only content. A moment is the turning effect of a force. Understanding moments is essential for explaining how levers, gears, and other rotating systems work in everyday life and in engineering.

---

What Is a Moment?

A moment is the turning effect of a force about a pivot (also called a fulcrum). When you push a door handle, turn a spanner, or use a see-saw, you are applying a moment.

The moment of a force is calculated using:

M = F x d

Where:

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

Key points:

• The moment depends on both the size of the force and the distance from the pivot.
• The distance must be the perpendicular (at right angles) distance from the pivot to the line of action of the force.
• Moments can be clockwise or anticlockwise.

Quantity	Value	Unit
Force applied to a spanner	20 N	N
Distance from pivot	0.3 m	m
Moment	20 x 0.3 = 6	Nm

Exam Tip: Always use the perpendicular distance in the moment equation. If the force is applied at an angle, the perpendicular distance is shorter than the actual distance from the pivot. This is a common source of errors in exam calculations.

---

The Principle of Moments

The principle of moments states:

When an object is in equilibrium (balanced), the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments about that pivot.

In equation form:

Sum of clockwise moments = Sum of anticlockwise moments

F1 x d1 = F2 x d2

This principle applies to any balanced system — see-saws, beams, levers, and many other situations.

Example: A Balanced See-Saw

A child of weight 400 N sits 2.0 m from the pivot of a see-saw. Where must a child of weight 500 N sit to balance the see-saw?

Using the principle of moments:

Clockwise moment = Anticlockwise moment

500 x d2 = 400 x 2.0

500 x d2 = 800

d2 = 800 / 500

d2 = 1.6 m from the pivot

graph LR
    subgraph "Balanced See-Saw"
        A["400 N"] ---|"2.0 m"| P["Pivot"]
        P ---|"1.6 m"| B["500 N"]
    end

    style P fill:#e67e22,color:#fff
    style A fill:#2980b9,color:#fff
    style B fill:#e74c3c,color:#fff

Exam Tip: When solving moment problems, always clearly identify the pivot point first. Then work out which forces cause clockwise moments and which cause anticlockwise moments. Set them equal and solve. Show all your working clearly for full marks.

---

Worked Examples

Example 1: Calculating a Moment

A force of 15 N is applied to a door handle at a perpendicular distance of 0.8 m from the hinge (pivot).

M = F x d M = 15 x 0.8 M = 12 Nm

Example 2: Finding the Force

A moment of 24 Nm is needed to turn a bolt. The spanner is 0.4 m long. What force is needed?

M = F x d 24 = F x 0.4 F = 24 / 0.4 F = 60 N

Example 3: Balancing with the Principle of Moments

A uniform beam of length 4.0 m is balanced on a pivot at its centre. A 60 N weight is placed 1.5 m from the pivot on the left side. What weight must be placed 1.0 m from the pivot on the right side to balance the beam?

Clockwise moment = Anticlockwise moment W x 1.0 = 60 x 1.5 W x 1.0 = 90 W = 90 N

---

Levers

A lever is a simple machine that uses a pivot (fulcrum) to multiply the effect of a force. Levers make it easier to do work by either:

• Increasing the force applied (at the expense of distance moved), or
• Increasing the distance moved (at the expense of force).

How Levers Work

A lever works by applying a small force at a large distance from the pivot to produce a large force at a small distance from the pivot (or vice versa).

The principle of moments explains why:

If F1 x d1 = F2 x d2, then a small force (F1) at a large distance (d1) can balance a large force (F2) at a small distance (d2).

Types of Levers

Class	Arrangement	Example
Class 1	Pivot between effort and load	See-saw, crowbar, scissors
Class 2	Load between pivot and effort	Wheelbarrow, nutcracker, bottle opener
Class 3	Effort between pivot and load	Tweezers, fishing rod, human forearm

graph LR
    subgraph "Class 1 Lever"
        E1["Effort"] ---|"d1"| P1["Pivot"] ---|"d2"| L1["Load"]
    end
    subgraph "Class 2 Lever"
        P2["Pivot"] ---|"d2"| L2["Load"] ---|"d1"| E2["Effort"]
    end
    subgraph "Class 3 Lever"
        P3["Pivot"] ---|"d1"| E3["Effort"] ---|"d2"| L3["Load"]
    end

    style P1 fill:#e67e22,color:#fff
    style P2 fill:#e67e22,color:#fff
    style P3 fill:#e67e22,color:#fff
    style E1 fill:#2980b9,color:#fff
    style E2 fill:#2980b9,color:#fff
    style E3 fill:#2980b9,color:#fff
    style L1 fill:#e74c3c,color:#fff
    style L2 fill:#e74c3c,color:#fff
    style L3 fill:#e74c3c,color:#fff

Exam Tip: [H] You may be asked to explain how a lever acts as a force multiplier. State that the effort is applied at a large distance from the pivot, and the principle of moments means a smaller effort force can balance a larger load force. Use M = F x d to support your explanation.

---

Gears

Gears are toothed wheels that mesh (interlock) together. When one gear turns, it causes the other gear to turn. Gears are used to:

• Transmit the turning effect of a force from one place to another.
• Multiply the force (a small gear driving a large gear increases the force but reduces the speed).
• Multiply the speed (a large gear driving a small gear increases the speed but reduces the force).
• Change the direction of rotation (meshing gears turn in opposite directions).

How Gears Relate to Moments

The moment transmitted by a gear depends on the radius of the gear:

M = F x r

Where r is the radius of the gear.

If a small gear (small radius) drives a large gear (large radius):

• The force is multiplied (the large gear exerts a greater force).
• The speed is reduced (the large gear turns more slowly).
• The large gear turns in the opposite direction to the small gear.

If a large gear drives a small gear:

• The speed is multiplied (the small gear turns faster).
• The force is reduced (the small gear exerts less force).

Driving Gear	Driven Gear	Effect on Force	Effect on Speed	Direction
Small	Large	Force multiplied	Speed reduced	Reversed
Large	Small	Force reduced	Speed multiplied	Reversed
Same size	Same size	No change	No change	Reversed

graph LR
    subgraph "Gear System"
        SG["Small gear (fast, low force)"] -->|"Meshes with"| LG["Large gear (slow, high force)"]
    end