Mechanical · Experiment

Torque & Levers — the Seesaw

Slide two masses along a balanced beam and find the exact spot where they cancel. Torque is force times distance — which is why a child far from the pivot can hold up an adult sitting close in.

mass 1 · torque τ₁ (counter-clockwise)mass 2 · torque τ₂ (clockwise)

Controls

Left torque τ₁ = m₁g·d₁—
Right torque τ₂ = m₂g·d₂—
Net torque (CW positive)—
Balance needs—
Balanced: m₁d₁ = m₂d₂ — the torques cancel.
About this experiment ›

What you are looking at

A rigid beam pivots on a central fulcrum, with a mass on each side that you can move and resize. If the turning effects cancel, the beam floats level; otherwise it tips toward the winning side and rests against its stop. The curved arrows show each side's torque and direction.

Torque: force times leverage

A force's ability to rotate something depends not just on how hard it pushes but on how far from the pivot it acts:
τ = F · d = m·g·d
Doubling the distance doubles the torque as surely as doubling the force — which is why door handles sit far from the hinges and wrenches have long handles.

Static equilibrium

The beam is in equilibrium when the net force and the net torque are both zero. The pivot supplies the force balance automatically, so the whole problem reduces to the torques:
m₁·g·d₁ = m₂·g·d₂  ⇒  m₁d₁ = m₂d₂
Gravity cancels out: only the mass-distance products matter. A 3 kg mass at 2 m holds a 4 kg mass at 1.5 m — 6 kg·m each side.

The law of the lever

This is Archimedes' machine: a small force far from the pivot balances (or lifts) a large force close in, trading distance for force. The mechanical advantage is d₁/d₂ — but as with the hydraulic press, energy is conserved: the far end sweeps a proportionally longer arc, so force × distance comes out even. "Give me a place to stand," Archimedes said, "and I shall move the Earth."

Things to try

Balance unequal masses by sliding the lighter one outward until m₁d₁ = m₂d₂ exactly. Then double both distances — still balanced, since both torques doubled. Park a 10 kg mass at 0.5 m and hold it with just 2.5 kg at 2 m: a 4× lever.