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 = 0.3 m0 → 700 rpm190 kg

A flywheel of mass 190 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 700 rpm. This takes 7 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.3 mn1 = 0 rpmn2 = 700 rpmt = 7 s
T = N·m
2.Easy
Or = 0.1 mL = 1.2 m1.3 m3.5 kg5.5 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 5.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.3 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1.2 mmsphere = 5.5 kgr = 0.1 md = 1.3 m
IO = kg·m²
3.Medium
ω = ?L = 0.7 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.7 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 = 9 kgL = 0.7 mg = 9.81 m/s²
ω = rad/s
4.Medium
L = 0.6 mm = 19.5 kgα

A uniform slender rod of mass 19.5 kg and length 0.6 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 = 19.5 kgL = 0.6 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 40°vs = 7.5 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7.5 m along the slope.

θ = 40°s = 7.5 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 30°a

A hollow sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 30°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. T = 179.1 N·m
  2. 2. IO = 11 kg·m²
  3. 3. ω = 6.484 rad/s
  4. 4. α = 24.53 rad/s²
  5. 5. v = 7.941 m/s
  6. 6. a = 2.943 m/s²

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