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 = 0.7 mGOd = 0.35 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 0.7 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 = 6.5 kgL = 0.7 md = 0.35 m
IO = kg·m²
2.Easy
k = 0.15 m0 → 1600 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 1600 rpm. The driving torque is a constant 36 N·m and friction can be ignored. How long t does this take?

m = 180 kgk = 0.15 mn1 = 0 rpmn2 = 1600 rpmT = 36 N·m
t = s
3.Medium
ω = ?4.5 kgL = 2.2 mm = 9 kg

A uniform slender rod of mass 9 kg and length 2.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 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 = 9 kgL = 2.2 mmball = 4.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
ω = ?L = 2 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 2 m is pinned at one end and released from rest in a horizontal position. 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 = 7.5 kgL = 2 mg = 9.81 m/s²
ω = rad/s
5.Hard
280 m/s45 g1.63 mL = 1.7 m8 kg

A uniform slender rod of mass 8 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 280 m/s hits the rod 1.63 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 8 kgL = 1.7 mm = 45 gv = 280 m/sd = 1.63 m
ω = rad/s
6.Hard
θ = 10°vs = 2.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2.5 m along the slope.

θ = 10°s = 2.5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 1.062 kg·m²
  2. 2. t = 18.85 s
  3. 3. ω = 3.271 rad/s
  4. 4. ω = 3.836 rad/s
  5. 5. ω = 2.624 rad/s
  6. 6. v = 2.467 m/s

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