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
R = 0.7 mn = 2900 rpm40 kg

A flywheel is a uniform solid disc of mass 40 kg and radius 0.7 m. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgR = 0.7 mn = 2900 rpm
Ek = kJ
2.Easy
k = 0.15 mn = 2400 rpm220 kg

A flywheel of mass 220 kg has a radius of gyration of 0.15 m about its axis. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 220 kgk = 0.15 mn = 2400 rpm
Ek = kJ
3.Medium
v = ?L = 2 mm = 4 kg

A uniform slender rod of mass 4 kg and length 2 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 4 kgL = 2 mg = 9.81 m/s²
v = m/s
4.Medium
n = 2800 rpmP = 113.5 kW

A shaft transmits 113.5 kW at 2800 rpm. Find the torque T in the shaft.

P = 113.5 kWn = 2800 rpm
T = N·m
5.Hard
9.5 m/sω

A solid sphere of mass 17 kg rolls without slipping at 9.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 17 kgv = 9.5 m/sI = (2/5)·m·r²
p = %
6.Hard
6 m/sω

A solid sphere of mass 10.5 kg rolls without slipping at 6 m/s. What percentage p of its total kinetic energy is rotational?

m = 10.5 kgv = 6 m/sI = (2/5)·m·r²
p = %

Answer key

  1. 1. Ek = 451.9 kJ
  2. 2. Ek = 156.3 kJ
  3. 3. v = 7.672 m/s
  4. 4. T = 387.1 N·m
  5. 5. p = 28.57 %
  6. 6. p = 28.57 %

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