The Wheel and Axle

The wheel and axle is a simple machine consisting of a large wheel attached to a smaller axle. Applying a force to the larger wheel produces a larger force at the axle, making it easier to turn heavy loads. Examples include steering wheels, door knobs, and screwdrivers.

What is a Wheel and Axle?

The wheel and axle is a simple machine made of a large wheel (or handle) attached to a smaller axle (rod). Both rotate together about the same point.

Input force: applied to the larger wheel
Output force: produced at the smaller axle

How it Works

The wheel and axle works like a circular lever. Because the wheel is larger than the axle, a small force applied at the rim of the wheel creates a larger force at the axle.

$\text{Mechanical Advantage} = \frac{R_{\text{wheel}}}{R_{\text{axle}}}$

Where $R$ is the radius.

A larger wheel compared to the axle → greater mechanical advantage → less effort needed.

Mechanical Advantage

A wheel has a radius of 30 cm and its axle has a radius of 5 cm.

$MA = \frac{30}{5} = 6$

This means the output force at the axle is 6 times the input force at the wheel.

Examples in Real Life

Example	Wheel	Axle
Steering wheel	Steering wheel rim	Steering column
Screwdriver	Handle (wide grip)	Shaft (tip)
Door knob	Knob (wide)	Door latch mechanism
Tap (faucet)	Handle	Tap stem
Bicycle wheel	Wheel rim	Hub/axle

Note

A screwdriver with a wider handle needs less force to turn a screw than one with a thin handle — the wider handle acts as a larger wheel.

Real world: Car steering wheel

A car's steering wheel has a radius of about 18 cm. The steering column (axle) has a radius of roughly 2 cm.

$MA = \frac{18}{2} = 9$

The driver applies a small force at the rim and the column exerts 9× that force on the steering rack — essential for turning heavy front wheels, especially at low speed.

Real world: Bicycle gears

On a bike, the chain ring (large wheel) has a radius of 10 cm and the rear sprocket (axle) has a radius of 2.5 cm.

$MA = \frac{10}{2.5} = 4$

Each pedal stroke moves the rear wheel 4 times as fast, converting the rider's leg force into forward motion efficiently.

Real world: Watermill wheel

Traditional watermills use a large wooden wheel turned by flowing water. The large wheel radius (e.g. 2 m) connects to a small millstone axle (radius 0.1 m), giving MA = 20. This converts a gentle water current into a powerful grinding force.

Tip Where do you see this in real life? Spin a door knob, grip a screwdriver handle, or turn a tap — every rotating tool with a wide grip is a wheel and axle. Notice that devices designed for speed (like a bicycle wheel) reverse the arrangement: a small force at the axle produces a fast-moving rim.

Practice Problems

A steering wheel has a radius of 25 cm and axle of 5 cm. What is the mechanical advantage?

Show answer

MA = R_wheel / R_axle = 25/5 = 5. The output force is 5 times the input force.

Why is a door knob wide rather than a thin rod?

Show answer

A wider knob acts as a larger wheel. This increases the mechanical advantage, requiring less force to operate the door latch.

A wheel and axle has MA = 8. If you apply 50 N to the wheel, what is the output force at the axle?

Show answer

Output force = MA × input force = 8 × 50 = 400 N.