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 = 0.35 mn = 2900 rpm120 kg

A flywheel of mass 120 kg has a radius of gyration of 0.35 m about its axis. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 120 kgk = 0.35 mn = 2900 rpm
Ek = kJ
2.Easy
k = 0.15 m200 → 1800 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.15 m is accelerated uniformly from 200 rpm to 1800 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 180 kgk = 0.15 mn1 = 200 rpmn2 = 1800 rpmt = 15 s
T = N·m
3.Medium
0 → 2300 rpmI = 26.5 kg·m²

A motor brings a flywheel with a moment of inertia of 26.5 kg·m² from rest up to 2300 rpm in 53 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 26.5 kg·m²n = 2300 rpmt = 53 s
Pavg = kW
4.Medium
1.5 kgaαM = 8 kgR = 0.25 m

A 1.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 kg and radius 0.25 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 = 1.5 kgM = 8 kgR = 0.25 mg = 9.81 m/s²
α = rad/s²
5.Hard
3.5 m/sω

A solid cylinder of mass 12 kg rolls without slipping at 3.5 m/s. Find its total kinetic energy Ek.

m = 12 kgv = 3.5 m/sI = ½·m·r²
Ek = J
6.Hard
140 m/s50 g0.5 mL = 0.5 m2.5 kg

A uniform slender rod of mass 2.5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 140 m/s hits the rod 0.5 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 2.5 kgL = 0.5 mm = 50 gv = 140 m/sd = 0.5 m
ω = rad/s

Answer key

  1. 1. Ek = 677.9 kJ
  2. 2. T = 45.24 N·m
  3. 3. Pavg = 14.5 kW
  4. 4. α = 10.7 rad/s²
  5. 5. Ek = 110.3 J
  6. 6. ω = 15.85 rad/s

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