Why a long spanner beats a short one, and how a seesaw finds its balance. Place weights on a beam and see the torque — the turning effect of each, τ = m·g·d. Set the mass and distance on each side and the beam tips toward the larger torque, sitting level only when the moments match: mL·dL = mR·dR. A small mass far out can balance a big mass close in — the principle behind every lever. It all runs on your device.
Trade mass for distance — a light weight far out balances a heavy weight close in.
Left torque—
Right torque—
Net torque—
State—
Distance matters as much as force. The turning effect of a weight is τ = m·g·d — proportional to both the mass and how far it sits from the pivot. That is why 2 kg at 1 m exactly balances 1 kg at 2 m, and why moving a weight outward tips the beam even though its mass hasn't changed. Balance is not about equal weights; it is about equal moments. Trade mass for distance and the beam settles level the instant mL·dL = mR·dR.
How It Works
A force, a distance, and the principle of moments that ties them together.
1
Torque = force × distance
Torque, or moment, is the turning effect of a force about a pivot: τ = F·d. For a hanging weight the force is its weight m·g, so τ = m·g·d. Push at the same spot with the same force but further from the pivot and the torque grows — the reason a longer wrench turns a stubborn bolt more easily.
2
The principle of moments
A beam is balanced — in rotational equilibrium — when the anticlockwise torque equals the clockwise torque. With one weight per side that is mL·dL = mR·dR, and g cancels out. Because distance counts, a light mass far from the pivot can hold up a heavy mass close to it.
3
Levers and mechanical advantage
That trade-off is exactly how a lever multiplies force: apply a modest effort far from the pivot to lift a large load near it, with mechanical advantage deffort/dload. Seesaws, wheelbarrows, crowbars and cranes all run on the same τ = F·d you are balancing here — slide the masses and distances and watch the beam find equilibrium.
What is torque?
Torque (a moment) is the turning effect of a force about a pivot. For a force F at perpendicular distance d, τ = F·d; for a weight, τ = m·g·d. The further out the force acts, the larger the torque — which is why a long spanner loosens a bolt a short one cannot. This simulator shows the torque from each weight on a balance beam.
When does a balance beam or lever balance?
When the total anticlockwise torque equals the total clockwise torque — the principle of moments. For one weight each side, mL·dL = mR·dR (g cancels). So a small mass far from the pivot can balance a large mass close to it: 2 kg at 1 m balances 1 kg at 2 m. The beam sits level exactly when the torques match.
What is the difference between torque and force?
A force is a straight-line push or pull; torque is its turning effect about a chosen pivot. The same force gives different torques depending on where it acts: zero if it passes through the pivot, more the further away it acts. Torque changes rotational motion the way force changes linear motion — hence τ = I·α, the rotational Newton's second law.
How does this relate to levers and simple machines?
A lever is the balance beam put to work: because torque depends on distance, a force far from the pivot can lift a much larger load close to it, with mechanical advantage deffort/dload. Levers, wrenches, seesaws, wheelbarrows and cranes all run on the same τ = F·d you are adjusting here.