SIMPLE MACHINES / WHEEL AND AXLE

Why does a bigger wheel make a small axle easier to turn?

Compare the effort at the wheel rim with a load acting at the axle.

ORIGINAL IDEAL EXAMPLE

100 N load
25 N effort

The wheel and axle rotate together. Tangential force at a larger radius produces more torque for the same effort.

Conceptual schematic; use the model below for parameter-linked geometry.

wheel-and-axle.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Wheel selected · related inputs are marked.

hand force25.00 N✓ passes

BASELINE INPUTS

load100 NaxleRadius25 mm1050

CALCULATED

effort25 N

mechanicalAdvantage4

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Wheel and axle: turn a large wheel to pull on a small axle
# Scope: Ideal rigid coaxial wheel and axle; tangential forces, no friction.
load = 100 N
wheelRadius = 100 mm in 80..200
axleRadius = 25 mm in 10..50
effort := load * axleRadius / wheelRadius [N]
mechanicalAdvantage := wheelRadius / axleRadius
part wheel "Wheel": cylinder wheelRadius, 10 mm at 0 mm, 0 mm, 30 mm
part axle "Axle": cylinder axleRadius, 60 mm
check hand force: effort <= 30 N
scenario larger wheel: wheelRadius = 150 mm

Calculated from your source · not saved

Baseline · Baseline

hand force25.00 N ✓ passes

larger wheel · larger wheel

hand force16.67 N ✓ passes

Calculated from the same .napkin source. Edits preview a temporary study and are not saved.

How the model works

The wheel and axle rotate together. Tangential force at a larger radius produces more torque for the same effort.

effort = load × axleRadius / wheelRadius

Try the alternative

A larger wheel reduces rim effort. The rim travels farther than the axle surface for the same rotation.

Choose a scenario, change an input, then inspect the equations and force check in Source.

Assumptions and limits

This is an ideal coaxial mechanism. Bearing friction, wheel strength and rope winding layers are omitted.