ONE FORMULA, ONE ANSWER
Atwood acceleration with pulley inertia calculator
Compute the acceleration of two hanging masses connected over a pulley with rotational inertia. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Acceleration a, positive when mass 2 descends
Enter values and select Calculate.
a = (m₂ − m₁)g / (m₁ + m₂ + I/r²)
Assumptions
Required: a massless inextensible rope, no slip at the pulley, freely moving hanging masses, and negligible axle friction and air drag. Positive acceleration means mass 2 descends; negative means mass 1 descends. I = 0 gives the ideal inertia-free pulley limit.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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