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
k = 0.5 mn = 1600 rpm280 kg

A flywheel of mass 280 kg has a radius of gyration of 0.5 m about its axis. It spins at 1600 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgk = 0.5 mn = 1600 rpm
Ek = kJ
2.Easy
k = 0.3 mn = 2200 rpm60 kg

A flywheel of mass 60 kg has a radius of gyration of 0.3 m about its axis. It spins at 2200 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgk = 0.3 mn = 2200 rpm
Ek = kJ
3.Medium
L = 2 mm = 18.5 kgα

A uniform slender rod of mass 18.5 kg and length 2 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 = 18.5 kgL = 2 mg = 9.81 m/s²
α = rad/s²
4.Medium
5 kgaαM = 3 kgR = 0.15 m

A 5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 3 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 acceleration a of the block.

m = 5 kgM = 3 kgR = 0.15 mg = 9.81 m/s²
a = m/s²
5.Hard
360 m/s30 g0.8 mL = 1.5 m5 kgφ

A uniform slender rod of mass 5 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 360 m/s hits the rod 0.8 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 = 5 kgL = 1.5 mm = 30 gv = 360 m/sd = 0.8 mg = 9.81 m/s²
φ = °
6.Hard
400 m/s5 g1.07 mL = 1.3 m4.5 kgφ

A uniform slender rod of mass 4.5 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 5 g bullet moving horizontally at 400 m/s hits the rod 1.07 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 = 4.5 kgL = 1.3 mm = 5 gv = 400 m/sd = 1.07 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 982.6 kJ
  2. 2. Ek = 143.3 kJ
  3. 3. α = 7.357 rad/s²
  4. 4. a = 7.546 m/s²
  5. 5. φ = 42.9 °
  6. 6. φ = 14.38 °

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