Mechanical Torque & Lever Physics Sandbox

Balance Scale Torque Simulator

Rigid Lever Fulcrum & Moment Arm Viewport
Drag masses onto notch hooks [-5 to +5]
System State PERFECT EQUILIBRIUM
Net Torque (Στ) 0.0 N·m
Beam Deflection 0.00°
Mass Repository (Drag to any notch or click to auto-mount) Active
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Orange (?kg)
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Azure (?kg)
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Emerald (?kg)
1
1 kg
2
2 kg
4
4 kg
8
8 kg
10
10 kg

Archimedes' Law of the Lever

For a lever in static rotational equilibrium, the algebraic sum of all torques about the pivot must equal zero (Στ = 0). Each mass generates torque τ = m × g × d, where d is the signed perpendicular distance from the fulcrum.

Deducing Unknown Masses

When an unknown mass X sits at notch d_x alongside known weights, solve via linear isolation: X = [ Σ(m_opp × d_opp) - Σ(m_same × d_same) ] / d_x.

Compound Mobile Levers

In multi-tier balances, lower beams transfer their total mass (M_tier = Σ m_children) upwards as a single point load hung from the parent notch.

Why a balance compares mass times distance

Read the explanation

The lever compares mass times notch distance on each side. The source puzzle puts four kilograms three notches left, plus an unknown one notch left. The right has eight kilograms two notches out and one kilogram four notches out. Its right moment is twenty kilogram notches; the known left moment is twelve. The missing eight makes the two sides equal. The steelyard preset makes the same point with unequal masses. Ten kilograms one notch from the pivot balance two kilograms five notches away. Both mass-distance products are ten. Gravity multiplies both sides by the same factor, so changing gravity changes the displayed moments but cannot change this balance condition. The compound preset has a subtle extra load in the actual calculation. Two lower masses of two kilograms each are joined by one kilogram of lower beam dead weight. That totals five, hanging three notches left: fifteen kilogram notches. Four kilograms three notches right give twelve. The code therefore produces a left-heavy net moment of minus twenty nine point four at default gravity, despite its balanced-looking preset description. Use the equation rail and exported specification to inspect moments and load positions. The solver button demonstrates the original orange-ball puzzle; it is not a general solver for every arrangement. Reset clears mounted masses rather than restoring the preset. The drawing uses normalized notches and approximate rotational dynamics, so treat it as an educational simulation rather than a calibrated mechanical design.

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