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 = 1.2 mGOd = 0.2 mm = 7 kg

A uniform slender rod of mass 7 kg and length 1.2 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 = 7 kgL = 1.2 md = 0.2 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.8 m1 m3.5 kg6.5 kg

A pendulum is made of a uniform slender rod (3.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 6.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 0.8 mmsphere = 6.5 kgr = 0.2 md = 1 m
IO = kg·m²
3.Medium
3.5 kgaαM = 4 kgR = 0.3 m

A 3.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4 kg and radius 0.3 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 2 m.

m = 3.5 kgM = 4 kgR = 0.3 mg = 9.81 m/s²h = 2 m
v = m/s
4.Medium
1 kgaαM = 10.5 kgR = 0.45 m

A 1 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 kg and radius 0.45 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 = 1 kgM = 10.5 kgR = 0.45 mg = 9.81 m/s²
T = N
5.Hard
θ = 40°vs = 3 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3 m along the slope.

θ = 40°s = 3 mI = m·r²g = 9.81 m/s²
v = m/s
6.Hard
580 m/s50 g0.2 mL = 0.5 m5 kg

A uniform slender rod of mass 5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 580 m/s hits the rod 0.2 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 5 kgL = 0.5 mm = 50 gv = 580 m/sd = 0.2 m
ω = rad/s

Answer key

  1. 1. IO = 1.12 kg·m²
  2. 2. IO = 7.351 kg·m²
  3. 3. v = 4.997 m/s
  4. 4. T = 8.24 N
  5. 5. v = 4.349 m/s
  6. 6. ω = 13.85 rad/s

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