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
L = 2.7 mGOd = 1.35 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.35 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9.5 kgL = 2.7 md = 1.35 m
IO = kg·m²
2.Easy
k = 0.45 m0 → 900 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.45 m is accelerated uniformly from rest to 900 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.45 mn1 = 0 rpmn2 = 900 rpmt = 17 s
T = N·m
3.Medium
n = 3000 rpmTb​ = 155 N·mI = 36 kg·m²

A flywheel with a moment of inertia of 36 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 155 N·m. How many revolutions N does the flywheel make before it stops?

I = 36 kg·m²n = 3000 rpmTb = 155 N·m
N = rev
4.Medium
L = 1.7 mm = 12 kgα

A uniform slender rod of mass 12 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 = 12 kgL = 1.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
540 m/s45 g0.89 mL = 1.1 m5 kg

A uniform slender rod of mass 5 kg and length 1.1 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 540 m/s hits the rod 0.89 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 5 kgL = 1.1 mm = 45 gv = 540 m/sd = 0.89 m
ω = rad/s
6.Hard
θ = 15°a

A solid cylinder rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 15°I = ½·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 23.09 kg·m²
  2. 2. T = 89.81 N·m
  3. 3. N = 1824 rev
  4. 4. atip = 14.71 m/s²
  5. 5. ω = 10.54 rad/s
  6. 6. μs = 0.08932

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