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 = 0.25 m900 → 1200 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.25 m is accelerated uniformly from 900 rpm to 1200 rpm. The driving torque is a constant 13 N·m and friction can be ignored. How long t does this take?

m = 180 kgk = 0.25 mn1 = 900 rpmn2 = 1200 rpmT = 13 N·m
t = s
2.Easy
R = 0.25 mn = 400 rpm30 kg

A flywheel is a uniform solid disc of mass 30 kg and radius 0.25 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgR = 0.25 mn = 400 rpm
Ek = kJ
3.Medium
4 kgaαM = 13 kgR = 0.15 m

A 4 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 13 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 = 4 kgM = 13 kgR = 0.15 mg = 9.81 m/s²
T = N
4.Medium
L = 1.8 mm = 5.5 kgα

A uniform slender rod of mass 5.5 kg and length 1.8 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 = 5.5 kgL = 1.8 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 10°a

A solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 10°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 35°a

A solid cylinder rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 35°I = ½·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. t = 27.19 s
  2. 2. Ek = 0.8225 kJ
  3. 3. T = 24.29 N
  4. 4. atip = 14.71 m/s²
  5. 5. μs = 0.05038
  6. 6. a = 3.751 m/s²

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