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 = 2.1 mGOd = 0.5 mm = 5 kg

A uniform slender rod of mass 5 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 2.1 md = 0.5 m
IO = kg·m²
2.Easy
L = 2.6 mGOd = 1.3 mm = 12 kg

A uniform slender rod of mass 12 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 1.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 12 kgL = 2.6 md = 1.3 m
IO = kg·m²
3.Medium
v = ?2 kgL = 0.6 mm = 7 kg

A uniform slender rod of mass 7 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 7 kgL = 0.6 mmball = 2 kgg = 9.81 m/s²
v = m/s
4.Medium
6 kgaαM = 6 kgR = 0.15 m

A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6 kg and radius 0.15 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 = 6 kgM = 6 kgR = 0.15 mg = 9.81 m/s²
T = N
5.Hard
θ = 40°as = 6.5 m

A solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 6.5 m down the slope?

θ = 40°I = ½·m·r²g = 9.81 m/s²s = 6.5 m
t = s
6.Hard
7.5 m/sω

A thin hoop of mass 6.5 kg rolls without slipping at 7.5 m/s. Find its rotational kinetic energy Erot.

m = 6.5 kgv = 7.5 m/sI = m·r²
Erot = J

Answer key

  1. 1. IO = 3.088 kg·m²
  2. 2. IO = 27.04 kg·m²
  3. 3. v = 3.865 m/s
  4. 4. T = 19.62 N
  5. 5. t = 1.759 s
  6. 6. Erot = 182.8 J

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