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 = 2000 rpm140 kg

A flywheel of mass 140 kg has a radius of gyration of 0.35 m about its axis. It spins at 2000 rpm. Find its kinetic energy Ek in kJ.

M = 140 kgk = 0.35 mn = 2000 rpm
Ek = kJ
2.Easy
L = 1.9 mGOd = 0.8 mm = 1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.9 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1.5 kgL = 1.9 md = 0.8 m
IO = kg·m²
3.Medium
n = 3000 rpmTb​ = 180 N·mI = 30.5 kg·m²

A flywheel with a moment of inertia of 30.5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 180 N·m. How long t does it take to stop?

I = 30.5 kg·m²n = 3000 rpmTb = 180 N·m
t = s
4.Medium
4.5 kgaαM = 12.5 kgR = 0.4 m

A 4.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 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 acceleration a of the block.

m = 4.5 kgM = 12.5 kgR = 0.4 mg = 9.81 m/s²
a = m/s²
5.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 =
6.Hard
400 m/s45 g1.62 mL = 1.8 m7 kgφ

A uniform slender rod of mass 7 kg and length 1.8 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 400 m/s hits the rod 1.62 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 7 kgL = 1.8 mm = 45 gv = 400 m/sd = 1.62 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 376.1 kJ
  2. 2. IO = 1.411 kg·m²
  3. 3. t = 53.23 s
  4. 4. a = 4.107 m/s²
  5. 5. μs = 0.104
  6. 6. φ = 83.44 °

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