Simple machines / lifting lab

Wheel & axle

TURN A WHEEL. LIFT A LOAD.

The wheel and axle turn together. A larger wheel needs less effort to lift the same crate.

Live values

3D lab

Make lifting easier

Guided experiment

Ready. Press Lift or Turn once.

Wheel radius R

Axle radius r

Crate mass

Effort needed

Ideal advantage

Teal wheel = effort. Amber axle = rope drum. Brown crate = load. Tap a part for a short explanation.

Speed & efficiency

Turning rate

Efficiency

Playback speed 1×

Mechanical sound

The motor-free model prescribes a steady handwheel speed and calculates the effort needed. It does not simulate acceleration.

View & focus tracking

Zoom 1×

3D viewing angle 30°

Inspect a part

Expand live values

Measurements & graph

A force–distance trade-off

Wheel and axle turn together.

The large wheel and small axle share one rigid shaft. One wheel turn is one axle turn. Their edges travel different distances.

Bigger wheel → less effort.

Apply a force farther from the centre and it produces more torque, the turning effect of a force.

Bigger axle → more rope per turn.

The load rises farther each turn, but lifting it needs more effort.

Equations

Load weight W = m × g

Torque τ = force × radius

Ideal advantage = R ÷ r

Actual advantage = η × R ÷ r

Effort F = m × g × r ÷ (η × R)

Hand distance = R × θ

Load rise = r × θ

Input work = F × hand distance

Useful work = m × g × rise

Efficiency η = useful work ÷ input work

R: wheel radius. r: axle radius. m: mass in kg. g = 9.81 m/s². θ: angle in radians. η: efficiency as a fraction, so 80% = 0.80. One full turn = 2π radians. Forces are in newtons, torque in N·m, and work in joules.

Learning objectives

Identify the wheel, axle, effort and load.
Predict how each radius changes effort and rope travel.
Connect torque balance to mechanical advantage.
Explain why the machine saves effort but does not create energy.
Relate efficiency to heat loss.

Try it

Compare a 30 cm wheel with a 60 cm wheel. Keep the axle and mass fixed.
Use Turn once with an 8 cm axle, then a 16 cm axle.
Double the mass. Does the ideal advantage change?
Reduce efficiency to 80%. Compare effort and work.

Explore further

Why do door knobs and steering wheels have large grips? What changes if your hand pushes toward the centre instead of tangentially?

Model and limits

This is a steady-speed lifting model, not a free acceleration model. The required tangential effort is calculated; pressing Lift prescribes rotation at the selected rate. The wheel and axle are rigidly coupled. Rope does not slip, stretch or build up extra layers. A constant effective efficiency represents total losses. A brake holds the load while paused and at the upper stop. Parameter changes start a new measurement run at the bottom to keep work and distance comparisons consistent. Energy totals exclude the initial placement of the crate. All illustrated forces are magnitudes. Arrow lengths are scaled for visibility.

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