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 = 1000 rpm120 kg

A flywheel is a uniform solid disc of mass 120 kg and radius 0.7 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.

M = 120 kgR = 0.7 mn = 1000 rpm
Ek = kJ
2.Easy
k = 0.6 m0 → 1600 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 1600 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.6 mn1 = 0 rpmn2 = 1600 rpmt = 11 s
T = N·m
3.Medium
11 kgaαM = 9.5 kgR = 0.45 m

An 11 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9.5 kg and radius 0.45 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 = 11 kgM = 9.5 kgR = 0.45 mg = 9.81 m/s²h = 1 m
v = m/s
4.Medium
L = 2.6 mm = 14 kgα

A uniform slender rod of mass 14 kg and length 2.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 14 kgL = 2.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 35°a

A hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 35°I = (2/3)·m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 20°a

A solid cylinder 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 = ½·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. Ek = 161.2 kJ
  2. 2. T = 438.7 N·m
  3. 3. v = 3.702 m/s
  4. 4. atip = 14.71 m/s²
  5. 5. μs = 0.2801
  6. 6. μs = 0.1213

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