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 = 0.2 mn = 1800 rpm220 kg

A flywheel of mass 220 kg has a radius of gyration of 0.2 m about its axis. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.

M = 220 kgk = 0.2 mn = 1800 rpm
Ek = kJ
2.Easy
R = 0.3 mn = 1200 rpm30 kg

A flywheel is a uniform solid disc of mass 30 kg and radius 0.3 m. It spins at 1200 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgR = 0.3 mn = 1200 rpm
Ek = kJ
3.Medium
14.5 kgaαM = 16.5 kgR = 0.15 m

A 14.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 16.5 kg and radius 0.15 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 14.5 kgM = 16.5 kgR = 0.15 mg = 9.81 m/s²
T = N
4.Medium
10.5 kgaαM = 9.5 kgR = 0.5 m

A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 1 m.

m = 10.5 kgM = 9.5 kgR = 0.5 mg = 9.81 m/s²h = 1 m
v = m/s
5.Hard
0.7 m0.15 mn1​ = 30 rpm

A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 30 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 4 kgr1 = 0.7 mr2 = 0.15 mn1 = 30 rpm
n2 = rpm
6.Hard
θ = 20°a

A solid sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 20°I = (2/5)·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. Ek = 156.3 kJ
  2. 2. Ek = 10.66 kJ
  3. 3. T = 51.58 N
  4. 4. v = 3.675 m/s
  5. 5. n2 = 96.79 rpm
  6. 6. μs = 0.104

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