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 = 1.4 mGOd = 0.6 mm = 3 kg

A uniform slender rod of mass 3 kg and length 1.4 m rotates about an axis O perpendicular to the rod, 0.6 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 1.4 md = 0.6 m
IO = kg·m²
2.Easy
L = 0.5 mGOd = 0.1 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9 kgL = 0.5 md = 0.1 m
IO = kg·m²
3.Medium
ω = ?2 kgL = 2.4 mm = 3.5 kg

A uniform slender rod of mass 3.5 kg and length 2.4 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 angular velocity ω of the rod as it swings through the vertical position.

m = 3.5 kgL = 2.4 mmball = 2 kgg = 9.81 m/s²
ω = rad/s
4.Medium
10.5 kgaαM = 9.5 kgR = 0.25 m

A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9.5 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 tension T in the cord.

m = 10.5 kgM = 9.5 kgR = 0.25 mg = 9.81 m/s²
T = N
5.Hard
100 m/s30 g0.98 mL = 1.2 m2.5 kgφ

A uniform slender rod of mass 2.5 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 100 m/s hits the rod 0.98 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 2.5 kgL = 1.2 mm = 30 gv = 100 m/sd = 0.98 mg = 9.81 m/s²
φ = °
6.Hard
θ = 10°as = 7.5 m

A thin hoop rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 7.5 m down the slope?

θ = 10°I = m·r²g = 9.81 m/s²s = 7.5 m
t = s

Answer key

  1. 1. IO = 1.57 kg·m²
  2. 2. IO = 0.2775 kg·m²
  3. 3. ω = 3.111 rad/s
  4. 4. T = 32.08 N
  5. 5. φ = 40.04 °
  6. 6. t = 4.197 s

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