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 mn = 1100 rpm180 kg

A flywheel of mass 180 kg has a radius of gyration of 0.6 m about its axis. It spins at 1100 rpm. Find its kinetic energy Ek in kJ.

M = 180 kgk = 0.6 mn = 1100 rpm
Ek = kJ
2.Easy
R = 0.55 mn = 900 rpm200 kg

A flywheel is a uniform solid disc of mass 200 kg and radius 0.55 m. It spins at 900 rpm. Find its kinetic energy Ek in kJ.

M = 200 kgR = 0.55 mn = 900 rpm
Ek = kJ
3.Medium
L = 0.8 mm = 5 kgα

A uniform slender rod of mass 5 kg and length 0.8 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 = 5 kgL = 0.8 mg = 9.81 m/s²
α = rad/s²
4.Medium
L = 1.4 mm = 19 kgα

A uniform slender rod of mass 19 kg and length 1.4 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 19 kgL = 1.4 mg = 9.81 m/s²
R = N
5.Hard
0.75 m0.15 mn1​ = 50 rpm

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.75 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 50 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3 kg·m²m = 2 × 1 kgr1 = 0.75 mr2 = 0.15 mn1 = 50 rpm
n2 = rpm
6.Hard
disc: 32 kgring: 15 kgn1​ = 400 rpm

A uniform solid disc (mass 32 kg, radius 0.5 m) spins freely at 400 rpm about a vertical frictionless shaft. A thin ring of mass 15 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 32 kgMring = 15 kgR = 0.5 mn1 = 400 rpm
n2 = rpm

Answer key

  1. 1. Ek = 429.9 kJ
  2. 2. Ek = 134.3 kJ
  3. 3. α = 18.39 rad/s²
  4. 4. R = 46.6 N
  5. 5. n2 = 67.73 rpm
  6. 6. n2 = 206.5 rpm

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