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 = 0.6 mn = 3000 rpm140 kg

A flywheel of mass 140 kg has a radius of gyration of 0.6 m about its axis. It spins at 3000 rpm. Find its kinetic energy Ek in kJ.

M = 140 kgk = 0.6 mn = 3000 rpm
Ek = kJ
2.Easy
L = 2.3 mGOd = 0.35 mm = 10.5 kg

A uniform slender rod of mass 10.5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10.5 kgL = 2.3 md = 0.35 m
IO = kg·m²
3.Medium
L = 0.5 mm = 13.5 kgα

A uniform slender rod of mass 13.5 kg and length 0.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 13.5 kgL = 0.5 mg = 9.81 m/s²
R = N
4.Medium
L = 0.6 mm = 4.5 kgα

A uniform slender rod of mass 4.5 kg and length 0.6 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 = 4.5 kgL = 0.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 35°vs = 3 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 3 m along the slope.

θ = 35°s = 3 mI = ½·m·r²g = 9.81 m/s²r = 0.15 m
ω = rad/s
6.Hard
320 m/s20 g0.83 mL = 1.7 m4 kgφ

A uniform slender rod of mass 4 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 320 m/s hits the rod 0.83 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 kgL = 1.7 mm = 20 gv = 320 m/sd = 0.83 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 2487 kJ
  2. 2. IO = 5.915 kg·m²
  3. 3. R = 33.11 N
  4. 4. atip = 14.71 m/s²
  5. 5. ω = 31.63 rad/s
  6. 6. φ = 26.98 °

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