Torque and Lever Balance — The Complete Physics Guide
A see-saw doesn't care how much weight is on each side — it cares how much torque each side produces, and torque depends on both the weight and how far it sits from the pivot. A small child can balance a much heavier adult simply by sitting further from the center. Lever Balance makes that trade-off the entire game.
This is the same physics behind a huge range of everyday tools — wrenches, crowbars, bottle openers, even your own forearm acting as a lever around your elbow — all of them trade force for distance, or distance for force, using exactly the balance condition this game asks you to solve.
Why Distance Multiplies Force
Torque is defined as τ = F × d — force multiplied by the perpendicular distance from the pivot to where the force is applied. This means the exact same force produces more torque the further it acts from the pivot. A wrench with a long handle doesn't make your hand stronger; it just lets the same hand-force act at a greater distance, producing far more torque on the bolt.
This is also why using a longer lever (or a longer wrench, or a bigger crowbar) feels like it gives you "more power" — it doesn't change how strong you are, it changes how effectively your strength gets converted into torque.
Worked Example — Balancing a See-Saw
Problem: A 10 kg weight sits 3 m from the pivot on the left. What mass placed 5 m from the pivot on the right balances the lever?
Left torque: 10 kg × 3 m = 30 kg·m
Setting torques equal: m × 5 = 30 → m = 6 kg — less than half the left weight, because it sits further out.
Worked Example — Multiple Weights
Problem: Weights of 5 kg at 2 m and 3 kg at 6 m sit on the left. What mass at 7 m balances them on the right?
Left torque: (5 × 2) + (3 × 6) = 10 + 18 = 28 kg·m
m × 7 = 28 → m = 4 kg
Real-World Applications
Tools: Wrenches, crowbars, and bottle openers are all levers designed to multiply force using exactly this trade-off between force and distance from a pivot point.
Construction cranes: A crane's counterweight is positioned at a calculated distance from the pivot specifically so its torque balances the torque of whatever load is being lifted — get this wrong and the crane tips over.
The human body: Your forearm is a lever pivoting at the elbow; your bicep applies force close to the joint, while the weight you're holding acts much further out — which is exactly why the same muscle can struggle to lift a dumbbell held at arm's length, even though it can lift far more when the elbow is bent.
Frequently Asked Questions
How do you calculate if a lever is balanced?+−
Multiply each weight by its distance from the pivot to get its torque, then compare the total torque on each side. The lever is balanced when both sides are exactly equal: Σ(m_left × d_left) = Σ(m_right × d_right).
Why does distance from the pivot matter as much as weight?+−
Torque is force multiplied by distance, so a small weight far from the pivot can produce the same torque as a large weight close to it. This is the entire principle behind using a lever to multiply force.
What happens if the torques aren’t equal?+−
The lever rotates toward the side with greater torque — the heavier-torque side goes down, the lighter-torque side goes up, exactly like a real see-saw.
Does the angle of the lever matter?+−
For weights hanging straight down on a lever close to horizontal, the simplified τ = F × d is accurate. As the angle changes significantly, the true formula τ = F × d × sin(θ) applies — see the Torque Calculator for the full version with angles.
How is this different from the Torque Calculator?+−
The Torque Calculator solves a single torque equation directly. This game asks you to balance a whole system — summing multiple weights on one side and solving for an unknown mass or distance on the other.