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
L = 2.8 mGOd = 0.95 mm = 3 kg

A uniform slender rod of mass 3 kg and length 2.8 m rotates about an axis O perpendicular to the rod, 0.95 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 2.8 md = 0.95 m
IO = kg·m²
2.Easy
k = 0.45 mn = 800 rpm280 kg

A flywheel of mass 280 kg has a radius of gyration of 0.45 m about its axis. It spins at 800 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgk = 0.45 mn = 800 rpm
Ek = kJ
3.Medium
13 kgaαM = 16.5 kgR = 0.4 m

A 13 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 16.5 kg and radius 0.4 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 = 13 kgM = 16.5 kgR = 0.4 mg = 9.81 m/s²
T = N
4.Medium
L = 1.1 mm = 6.5 kgα

A uniform slender rod of mass 6.5 kg and length 1.1 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 = 6.5 kgL = 1.1 mg = 9.81 m/s²
R = N
5.Hard
θ = 35°vs = 1.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.1 m. Find its angular velocity ω after it has rolled 1.5 m along the slope.

θ = 35°s = 1.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.1 m
ω = rad/s
6.Hard
0.65 m0.35 mn1​ = 35 rpm

A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 2.5 kg·m² about the axis. They turn at 35 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 2.5 kg·m²m = 2 × 4 kgr1 = 0.65 mr2 = 0.35 mn1 = 35 rpm
n2 = rpm

Answer key

  1. 1. IO = 4.667 kg·m²
  2. 2. Ek = 199 kJ
  3. 3. T = 49.51 N
  4. 4. R = 15.94 N
  5. 5. ω = 34.72 rad/s
  6. 6. n2 = 59.14 rpm

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