Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
k = 0.5 m900 → 1900 rpm130 kg

A flywheel of mass 130 kg with a radius of gyration of 0.5 m is accelerated uniformly from 900 rpm to 1900 rpm. The driving torque is a constant 240 N·m and friction can be ignored. How long t does this take?

m = 130 kgk = 0.5 mn1 = 900 rpmn2 = 1900 rpmT = 240 N·m
t = s
2.Easy
k = 0.6 m0 → 500 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 500 rpm. The driving torque is a constant 84 N·m and friction can be ignored. How long t does this take?

m = 40 kgk = 0.6 mn1 = 0 rpmn2 = 500 rpmT = 84 N·m
t = s
3.Medium
n = 2400 rpmP = 110 kW

A shaft transmits 110 kW at 2400 rpm. Find the torque T in the shaft.

P = 110 kWn = 2400 rpm
T = N·m
4.Medium
n = 800 rpmP = 99.5 kW

A shaft transmits 99.5 kW at 800 rpm. Find the torque T in the shaft.

P = 99.5 kWn = 800 rpm
T = N·m
5.Hard
8.5 m/sω

A solid cylinder of mass 18.5 kg rolls without slipping at 8.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 18.5 kgv = 8.5 m/sI = ½·m·r²
p = %
6.Hard
6 m/sω

A solid sphere of mass 14 kg rolls without slipping at 6 m/s. Find its total kinetic energy Ek.

m = 14 kgv = 6 m/sI = (2/5)·m·r²
Ek = J

Answer key

  1. 1. t = 14.18 s
  2. 2. t = 8.976 s
  3. 3. T = 437.7 N·m
  4. 4. T = 1188 N·m
  5. 5. p = 33.33 %
  6. 6. Ek = 352.8 J

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