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 = 0.2 m0 → 1100 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1100 rpm. This takes 4 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.2 mn1 = 0 rpmn2 = 1100 rpmt = 4 s
T = N·m
2.Easy
k = 0.4 m800 → 1700 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.4 m is accelerated uniformly from 800 rpm to 1700 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.

m = 70 kgk = 0.4 mn1 = 800 rpmn2 = 1700 rpmt = 17 s
T = N·m
3.Medium
n = 800 rpmTb​ = 110 N·mI = 19.5 kg·m²

A flywheel with a moment of inertia of 19.5 kg·m² spins at 800 rpm. A brake applies a constant friction torque of 110 N·m. How long t does it take to stop?

I = 19.5 kg·m²n = 800 rpmTb = 110 N·m
t = s
4.Medium
ω = ?2 kgL = 0.5 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 7.5 kgL = 0.5 mmball = 2 kgg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 30°vs = 10 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 10 m along the slope.

θ = 30°s = 10 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 25°vs = 9 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. Its radius is 0.4 m. Find its angular velocity ω after it has rolled 9 m along the slope.

θ = 25°s = 9 mI = m·r²g = 9.81 m/s²r = 0.4 m
ω = rad/s

Answer key

  1. 1. T = 92.15 N·m
  2. 2. T = 62.09 N·m
  3. 3. t = 14.85 s
  4. 4. ω = 7.081 rad/s
  5. 5. v = 7.672 m/s
  6. 6. ω = 15.27 rad/s

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