Levers & Gears

Levers Basics

A lever is a simple machine that helps us do work more easily by turning a small force into a larger force. It consists of three main parts:

• Effort: The force you apply to the lever.
• Load: The force exerted by the object you want to move or lift.
• Pivot (or fulcrum): The fixed point around which the lever turns.

Levers work by rotating around the pivot, and the effort and load act at different distances from this pivot.

Levers help increase the mechanical advantage, which is the ratio of the load force to the effort force. Mechanical advantage depends on the distances of the effort and load from the pivot: a longer effort arm compared to the load arm means a greater mechanical advantage, making work easier.

Types of Levers

There are three types of levers, classified by the relative positions of the effort, load, and pivot:

• First-class lever: The pivot is between the effort and the load.
  Example: A seesaw or crowbar.
• Second-class lever: The load is between the effort and the pivot.
  Example: A wheelbarrow.
• Third-class lever: The effort is between the load and the pivot.
  Example: Tweezers or a fishing rod.

Each type of lever changes the size and direction of the forces differently, making tasks easier depending on the setup.

For example, a first-class lever like a crowbar allows you to apply a small effort far from the pivot to lift a heavy load close to the pivot.

Moments and Principle of Moments

A moment is the turning effect of a force about a pivot. It depends on two things:

• The size of the force applied (in newtons, N)
• The perpendicular distance from the pivot to the line of action of the force (in metres, m)

The formula for a moment is:

$$\text{Moment} = \text{Force} \times \text{Perpendicular distance from pivot}$$

Moments are measured in newton-metres (N·m).

For example, if you push a door with a force of 10 N at a point 0.5 m from the hinges (pivot), the moment is:

\[ \text{Moment} = 10 \times 0.5 = 5 \text{ N·m} \]

Moments can turn objects in two directions:

• Clockwise moments: Turning in the same direction as clock hands.
• Anticlockwise moments: Turning opposite to clock hands.

The principle of moments states that for an object to be in equilibrium (balanced and not turning), the total clockwise moments must equal the total anticlockwise moments:

$$\text{Total clockwise moments} = \text{Total anticlockwise moments}$$

This principle is used to solve problems involving levers and seesaws.

For instance, if a seesaw is balanced, and a child weighing 300 N sits 2 m from the pivot, another child weighing 200 N must sit at a distance $d$ such that:

$$300 \times 2 = 200 \times d$$

$$d = \frac{300 \times 2}{200} = 3 \text{ m}$$

Gears and Gear Ratios

Gears are toothed wheels that interlock to transmit rotational force (turning effect) from one shaft to another.

They are used to change the size of a force, the speed of rotation, or the direction of rotation in machines.

Gear ratio compares the sizes of two gears and determines how the speed and force change between them. It is calculated by comparing the number of teeth on each gear:

$$\text{Gear ratio} = \frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driving gear}}$$

If the driven gear has more teeth than the driving gear, the output force is increased but the speed decreases. If the driven gear has fewer teeth, the speed increases but the force decreases.

For example, if a driving gear with 20 teeth turns a driven gear with 60 teeth, the gear ratio is:

$$\frac{60}{20} = 3$$

This means the driven gear turns slower but with three times the force.

Gears also change the direction of rotation. When two gears mesh, they rotate in opposite directions.

If a third gear is added between two gears (an idler gear), it reverses the direction again so the first and last gears rotate in the same direction.

For example, a bicycle uses gears to change the pedalling force and speed. Low gears (small driving gear, large driven gear) make pedalling easier uphill by increasing force but reducing speed.

A car’s gearbox uses gears to adjust speed and torque depending on driving conditions.

Understanding gear ratios helps in designing machines that balance speed and force efficiently.

Example: Calculate the moment of a force of 15 N applied 0.4 m from the pivot.

Using the formula $\text{Moment} = \text{Force} \times \text{Distance}$,

\[ \text{Moment} = 15 \times 0.4 = 6 \text{ N·m} \]

Learning example: Calculate the moment when a force of 12 N is applied at a perpendicular distance of 0.3 m from a pivot.

Solution: \( \text{Moment} = 12 \times 0.3 = 3.6 \text{ N·m} \)