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
Or = 0.1 mL = 1 m1.1 m4 kg7 kg

A pendulum is made of a uniform slender rod (4 kg, 1 m long) pivoted at its top end O, with a solid sphere of mass 7 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 1 mmsphere = 7 kgr = 0.1 md = 1.1 m
IO = kg·m²
2.Easy
L = 1.3 mGOd = 0.3 mm = 3.5 kg

A uniform slender rod of mass 3.5 kg and length 1.3 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3.5 kgL = 1.3 md = 0.3 m
IO = kg·m²
3.Medium
L = 2.1 mm = 4.5 kgα

A uniform slender rod of mass 4.5 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 = 4.5 kgL = 2.1 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 1200 rpmP = 180 kW

A shaft transmits 180 kW at 1200 rpm. Find the torque T in the shaft.

P = 180 kWn = 1200 rpm
T = N·m
5.Hard
220 m/s5 g2 mL = 2 m6 kg

A uniform slender rod of mass 6 kg and length 2 m hangs at rest from a frictionless pivot at its top end. A 5 g bullet moving horizontally at 220 m/s hits the rod 2 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 6 kgL = 2 mm = 5 gv = 220 m/sd = 2 m
ω = rad/s
6.Hard
560 m/s20 g0.32 mL = 0.8 m9 kg

A uniform slender rod of mass 9 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 560 m/s hits the rod 0.32 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 9 kgL = 0.8 mm = 20 gv = 560 m/sd = 0.32 m
ω = rad/s

Answer key

  1. 1. IO = 9.831 kg·m²
  2. 2. IO = 0.8079 kg·m²
  3. 3. α = 7.007 rad/s²
  4. 4. T = 1432 N·m
  5. 5. ω = 0.2743 rad/s
  6. 6. ω = 1.865 rad/s

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