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 = 0.6 m400 → 2300 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.6 m is accelerated uniformly from 400 rpm to 2300 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.

m = 10 kgk = 0.6 mn1 = 400 rpmn2 = 2300 rpmt = 30 s
T = N·m
2.Easy
L = 2.2 mGOd = 0.25 mm = 8 kg

A uniform slender rod of mass 8 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 8 kgL = 2.2 md = 0.25 m
IO = kg·m²
3.Medium
v = ?4 kgL = 1 mm = 2 kg

A uniform slender rod of mass 2 kg and length 1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 2 kgL = 1 mmball = 4 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 1600 rpmTb​ = 160 N·mI = 36.5 kg·m²

A flywheel with a moment of inertia of 36.5 kg·m² spins at 1600 rpm. A brake applies a constant friction torque of 160 N·m. How many revolutions N does the flywheel make before it stops?

I = 36.5 kg·m²n = 1600 rpmTb = 160 N·m
N = rev
5.Hard
θ = 25°vs = 8.5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8.5 m along the slope.

θ = 25°s = 8.5 mI = m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 25°vs = 4 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 4 m along the slope.

θ = 25°s = 4 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. T = 23.88 N·m
  2. 2. IO = 3.727 kg·m²
  3. 3. v = 4.585 m/s
  4. 4. N = 509.6 rev
  5. 5. v = 5.936 m/s
  6. 6. v = 4.702 m/s

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