How to use this calculator
Choose a single hanging block or two blocks over the pulley (an Atwood machine). Give the pulley as a solid disk, a thin ring, a radius of gyration or its moment of inertia. The rope does not slip, so a = αR.
Formulas
Single blocka = mg / (m + I/R²)
Atwooda = (m1 − m2)g / (m1 + m2 + I/R²)
Pulley(T1 − T2)R = Iα, a = αR
Worked example
2 kg block on a rope wound on a 4 kg solid disk of radius 0.2 m
- I = ½MR² = ½(4)(0.2)² = 0.08 kg·m², so I/R² = 2 kg.
- a = (2)(9.81)/(2 + 2) = 4.905 m/s².
- T = m(g − a) = 2(9.81 − 4.905) = 9.81 N, and α = a/R = 24.5 rad/s².
Frequently asked questions
Why is the tension less than the weight?
The block accelerates downward, so its weight must be larger than the rope force. The difference is what spins up the pulley.
What if the pulley is massless?
Set its mass to zero: I/R² vanishes and the answers become the textbook massless-pulley results.