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 = 0.45 m0 → 500 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.45 m is accelerated uniformly from rest to 500 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.45 mn1 = 0 rpmn2 = 500 rpmt = 11 s
T = N·m
2.Easy
Or = 0.05 mL = 0.9 m0.95 m4.5 kg4.5 kg

A pendulum is made of a uniform slender rod (4.5 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.95 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 0.9 mmsphere = 4.5 kgr = 0.05 md = 0.95 m
IO = kg·m²
3.Medium
6 kgaαM = 2.5 kgR = 0.4 m

A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 2.5 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 6 kgM = 2.5 kgR = 0.4 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 1800 rpmTb​ = 35 N·mI = 3 kg·m²

A flywheel with a moment of inertia of 3 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 35 N·m. How long t does it take to stop?

I = 3 kg·m²n = 1800 rpmTb = 35 N·m
t = s
5.Hard
2.5 m/sω

A solid cylinder of mass 16.5 kg rolls without slipping at 2.5 m/s. Find its rotational kinetic energy Erot.

m = 16.5 kgv = 2.5 m/sI = ½·m·r²
Erot = J
6.Hard
580 m/s10 g0.29 mL = 0.6 m9.5 kg

A uniform slender rod of mass 9.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 580 m/s hits the rod 0.29 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 9.5 kgL = 0.6 mm = 10 gv = 580 m/sd = 0.29 m
ω = rad/s

Answer key

  1. 1. T = 38.56 N·m
  2. 2. IO = 5.281 kg·m²
  3. 3. α = 20.3 rad/s²
  4. 4. t = 16.16 s
  5. 5. Erot = 25.78 J
  6. 6. ω = 1.474 rad/s

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