Atwood Machine Acceleration
Also known as two masses over a pulley
Worked example: 3 kg vs 2 kg → 1.96133 m/s² — press Try an example to run it live, then adjust anything.
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Atwood Machine Acceleration explained
Hang two masses over a light, frictionless pulley and only the difference in weight drives the system, while the total mass has to be accelerated — giving a = (m₁ − m₂)g ⁄ (m₁ + m₂). With 3 kg against 2 kg the acceleration is (1 ⁄ 5) × 9.80665 ≈ 1.96 m/s², a fifth of free fall. Make the masses nearly equal and the acceleration becomes as gentle as you like, which is precisely the point: George Atwood built his machine in 1784 to slow gravity down enough to verify Newton's laws with the crude clocks of the day.
Two sanity checks fall out immediately. Equal masses give a = 0, the system balances. Let m₂ → 0 and a → g, plain free fall. The idealisation to watch is the pulley: a real one has rotational inertia and bearing friction, so measured accelerations run a few percent low, and the rope's own mass matters once the masses are small. Elevator counterweights are the industrial version of the same trick — balancing most of the car's weight so the motor only has to handle the difference.
Atwood Machine Acceleration formula
- = Acceleration (m/s²)
- = Heavier mass (kg)
- = Lighter mass (kg)
Missing one of these? Work it out first, then come back
- Acceleration — Newton's Second Law, Final Velocity (Uniform Acceleration)
- Heavier mass — Newton's Second Law, Kinetic Energy
- Lighter mass — Newton's Second Law, Kinetic Energy