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 = 0.4 mGOd = 0.2 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.4 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9 kgL = 0.4 md = 0.2 m
IO = kg·m²
2.Easy
L = 2.2 mGOd = 1 mm = 4 kg

A uniform slender rod of mass 4 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4 kgL = 2.2 md = 1 m
IO = kg·m²
3.Medium
L = 1.1 mm = 10.5 kgα

A uniform slender rod of mass 10.5 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 acceleration atip of the free end just after release.

m = 10.5 kgL = 1.1 mg = 9.81 m/s²
atip = m/s²
4.Medium
12.5 kgaαM = 5.5 kgR = 0.4 m

A 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 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 = 12.5 kgM = 5.5 kgR = 0.4 mg = 9.81 m/s²
T = N
5.Hard
θ = 10°vs = 8.5 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 8.5 m along the slope.

θ = 10°s = 8.5 mI = ½·m·r²g = 9.81 m/s²r = 0.35 m
ω = rad/s
6.Hard
140 m/s25 g0.96 mL = 1.4 m3.5 kg

A uniform slender rod of mass 3.5 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 140 m/s hits the rod 0.96 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 3.5 kgL = 1.4 mm = 25 gv = 140 m/sd = 0.96 m
ω = rad/s

Answer key

  1. 1. IO = 0.48 kg·m²
  2. 2. IO = 5.613 kg·m²
  3. 3. atip = 14.71 m/s²
  4. 4. T = 22.11 N
  5. 5. ω = 12.55 rad/s
  6. 6. ω = 1.455 rad/s

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