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
R = 0.8 mn = 2400 rpm60 kg

A flywheel is a uniform solid disc of mass 60 kg and radius 0.8 m. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgR = 0.8 mn = 2400 rpm
Ek = kJ
2.Easy
k = 0.4 m0 → 400 rpm190 kg

A flywheel of mass 190 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 400 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.4 mn1 = 0 rpmn2 = 400 rpmt = 17 s
T = N·m
3.Medium
n = 1700 rpmP = 188 kW

A shaft transmits 188 kW at 1700 rpm. Find the torque T in the shaft.

P = 188 kWn = 1700 rpm
T = N·m
4.Medium
L = 1.9 mm = 12.5 kgα

A uniform slender rod of mass 12.5 kg and length 1.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 12.5 kgL = 1.9 mg = 9.81 m/s²
α = rad/s²
5.Hard
3 m/sω

A solid sphere of mass 16.5 kg rolls without slipping at 3 m/s. Find its rotational kinetic energy Erot.

m = 16.5 kgv = 3 m/sI = (2/5)·m·r²
Erot = J
6.Hard
θ = 15°vs = 4 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 4 m along the slope.

θ = 15°s = 4 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. Ek = 606.4 kJ
  2. 2. T = 74.91 N·m
  3. 3. T = 1056 N·m
  4. 4. α = 7.745 rad/s²
  5. 5. Erot = 29.7 J
  6. 6. ω = 13.96 rad/s

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