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 = 0.15 m0 → 1100 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 1100 rpm. This takes 5 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.15 mn1 = 0 rpmn2 = 1100 rpmt = 5 s
T = N·m
2.Easy
k = 0.25 m800 → 2000 rpm190 kg

A flywheel of mass 190 kg with a radius of gyration of 0.25 m is accelerated uniformly from 800 rpm to 2000 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.25 mn1 = 800 rpmn2 = 2000 rpmt = 11 s
T = N·m
3.Medium
L = 2.5 mm = 5.5 kgα

A uniform slender rod of mass 5.5 kg and length 2.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 5.5 kgL = 2.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
ω = ?L = 2 mm = 2 kg

A uniform slender rod of mass 2 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 angular velocity ω of the rod as it swings through the vertical position.

m = 2 kgL = 2 mg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 10°vs = 3.5 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3.5 m along the slope.

θ = 10°s = 3.5 mI = ½·m·r²g = 9.81 m/s²
v = m/s
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. T = 41.47 N·m
  2. 2. T = 135.7 N·m
  3. 3. α = 5.886 rad/s²
  4. 4. ω = 3.836 rad/s
  5. 5. v = 2.82 m/s
  6. 6. μs = 0.104

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