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 = 0.55 m0 → 1300 rpm170 kg

A flywheel of mass 170 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 1300 rpm. This takes 7 s. Ignoring friction, find the constant torque T needed.

m = 170 kgk = 0.55 mn1 = 0 rpmn2 = 1300 rpmt = 7 s
T = N·m
2.Easy
Or = 0.1 mL = 0.9 m1 m0.5 kg10 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.9 mmsphere = 10 kgr = 0.1 md = 1 m
IO = kg·m²
3.Medium
L = 0.9 mm = 13.5 kgα

A uniform slender rod of mass 13.5 kg and length 0.9 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 = 13.5 kgL = 0.9 mg = 9.81 m/s²
atip = m/s²
4.Medium
L = 1.7 mm = 18.5 kgα

A uniform slender rod of mass 18.5 kg and length 1.7 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 = 18.5 kgL = 1.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
4 m/sω

A solid cylinder of mass 11 kg rolls without slipping at 4 m/s. What percentage p of its total kinetic energy is rotational?

m = 11 kgv = 4 m/sI = ½·m·r²
p = %
6.Hard
θ = 25°vs = 3 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3 m along the slope.

θ = 25°s = 3 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. T = 1000 N·m
  2. 2. IO = 10.17 kg·m²
  3. 3. atip = 14.71 m/s²
  4. 4. atip = 14.71 m/s²
  5. 5. p = 33.33 %
  6. 6. v = 4.072 m/s

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