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 m0 → 800 rpm30 kg

A flywheel of mass 30 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 800 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.35 mn1 = 0 rpmn2 = 800 rpmt = 11 s
T = N·m
2.Easy
L = 1.8 mGOd = 0.3 mm = 12 kg

A uniform slender rod of mass 12 kg and length 1.8 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 12 kgL = 1.8 md = 0.3 m
IO = kg·m²
3.Medium
4 kgaαM = 8 kgR = 0.5 m

A 4 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 4 kgM = 8 kgR = 0.5 mg = 9.81 m/s²
T = N
4.Medium
n = 1200 rpmTb​ = 25 N·mI = 10 kg·m²

A flywheel with a moment of inertia of 10 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 25 N·m. How long t does it take to stop?

I = 10 kg·m²n = 1200 rpmTb = 25 N·m
t = s
5.Hard
θ = 25°vs = 6 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 6 m along the slope.

θ = 25°s = 6 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 40°a

A hollow sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 40°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. T = 27.99 N·m
  2. 2. IO = 4.32 kg·m²
  3. 3. T = 19.62 N
  4. 4. t = 50.27 s
  5. 5. v = 5.759 m/s
  6. 6. a = 3.783 m/s²

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