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 = 0.5 mn = 1400 rpm60 kg

A flywheel of mass 60 kg has a radius of gyration of 0.5 m about its axis. It spins at 1400 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgk = 0.5 mn = 1400 rpm
Ek = kJ
2.Easy
k = 0.3 m0 → 600 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 600 rpm. The driving torque is a constant 3.3 N·m and friction can be ignored. How long t does this take?

m = 10 kgk = 0.3 mn1 = 0 rpmn2 = 600 rpmT = 3.3 N·m
t = s
3.Medium
n = 500 rpmTb​ = 25 N·mI = 29 kg·m²

A flywheel with a moment of inertia of 29 kg·m² spins at 500 rpm. A brake applies a constant friction torque of 25 N·m. How long t does it take to stop?

I = 29 kg·m²n = 500 rpmTb = 25 N·m
t = s
4.Medium
9 kgaαM = 8 kgR = 0.3 m

A 9 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 kg and radius 0.3 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 9 kgM = 8 kgR = 0.3 mg = 9.81 m/s²
α = rad/s²
5.Hard
9.5 m/sω

A solid cylinder of mass 20 kg rolls without slipping at 9.5 m/s. Find its rotational kinetic energy Erot.

m = 20 kgv = 9.5 m/sI = ½·m·r²
Erot = J
6.Hard
θ = 25°vs = 3.5 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. Its radius is 0.25 m. Find its angular velocity ω after it has rolled 3.5 m along the slope.

θ = 25°s = 3.5 mI = ½·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. Ek = 161.2 kJ
  2. 2. t = 17.14 s
  3. 3. t = 60.74 s
  4. 4. α = 22.64 rad/s²
  5. 5. Erot = 451.3 J
  6. 6. ω = 17.59 rad/s

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