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 = 2.7 mGOd = 0.95 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 2.7 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 = 9.5 kgL = 2.7 md = 0.95 m
IO = kg·m²
2.Easy
L = 2.6 mGOd = 0.75 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.75 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 6.5 kgL = 2.6 md = 0.75 m
IO = kg·m²
3.Medium
L = 2.1 mm = 10.5 kgα

A uniform slender rod of mass 10.5 kg and length 2.1 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 = 10.5 kgL = 2.1 mg = 9.81 m/s²
α = rad/s²
4.Medium
1.5 kgaαM = 8.5 kgR = 0.25 m

A 1.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 4.5 m.

m = 1.5 kgM = 8.5 kgR = 0.25 mg = 9.81 m/s²h = 4.5 m
v = m/s
5.Hard
θ = 35°vs = 3.5 m

A solid cylinder 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 0.25 m. Find its angular velocity ω after it has rolled 3.5 m along the slope.

θ = 35°s = 3.5 mI = ½·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s
6.Hard
θ = 20°as = 7 m

A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 7 m down the slope?

θ = 20°I = ½·m·r²g = 9.81 m/s²s = 7 m
t = s

Answer key

  1. 1. IO = 14.35 kg·m²
  2. 2. IO = 7.318 kg·m²
  3. 3. α = 7.007 rad/s²
  4. 4. v = 4.799 m/s
  5. 5. ω = 20.5 rad/s
  6. 6. t = 2.502 s

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