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 = 0.4 m400 → 900 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.4 m is accelerated uniformly from 400 rpm to 900 rpm. This takes 2 s. Ignoring friction, find the constant torque T needed.

m = 10 kgk = 0.4 mn1 = 400 rpmn2 = 900 rpmt = 2 s
T = N·m
2.Easy
R = 0.3 mn = 400 rpm280 kg

A flywheel is a uniform solid disc of mass 280 kg and radius 0.3 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgR = 0.3 mn = 400 rpm
Ek = kJ
3.Medium
L = 2.3 mm = 20 kgα

A uniform slender rod of mass 20 kg and length 2.3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 20 kgL = 2.3 mg = 9.81 m/s²
R = N
4.Medium
L = 2.6 mm = 1.5 kgα

A uniform slender rod of mass 1.5 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 = 1.5 kgL = 2.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 25°a

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 25°I = m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 30°as = 9 m

A solid cylinder rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9 m down the slope?

θ = 30°I = ½·m·r²g = 9.81 m/s²s = 9 m
t = s

Answer key

  1. 1. T = 41.89 N·m
  2. 2. Ek = 11.05 kJ
  3. 3. R = 49.05 N
  4. 4. atip = 14.71 m/s²
  5. 5. μs = 0.2332
  6. 6. t = 2.346 s

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