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 = 2.3 mGOd = 1.15 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 1.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5.5 kgL = 2.3 md = 1.15 m
IO = kg·m²
2.Easy
k = 0.15 m600 → 1100 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.15 m is accelerated uniformly from 600 rpm to 1100 rpm. The driving torque is a constant 16 N·m and friction can be ignored. How long t does this take?

m = 160 kgk = 0.15 mn1 = 600 rpmn2 = 1100 rpmT = 16 N·m
t = s
3.Medium
6.5 kgaαM = 12.5 kgR = 0.1 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 kg and radius 0.1 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 = 6.5 kgM = 12.5 kgR = 0.1 mg = 9.81 m/s²
T = N
4.Medium
14 kgaαM = 12.5 kgR = 0.4 m

A 14 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 kg and radius 0.4 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 3 m.

m = 14 kgM = 12.5 kgR = 0.4 mg = 9.81 m/s²h = 3 m
v = m/s
5.Hard
2.5 m/sω

A hollow sphere of mass 13 kg rolls without slipping at 2.5 m/s. Find its total kinetic energy Ek.

m = 13 kgv = 2.5 m/sI = (2/3)·m·r²
Ek = J
6.Hard
600 m/s40 g0.58 mL = 0.7 m1 kg

A uniform slender rod of mass 1 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 600 m/s hits the rod 0.58 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1 kgL = 0.7 mm = 40 gv = 600 m/sd = 0.58 m
ω = rad/s

Answer key

  1. 1. IO = 9.698 kg·m²
  2. 2. t = 11.78 s
  3. 3. T = 31.26 N
  4. 4. v = 6.379 m/s
  5. 5. Ek = 67.71 J
  6. 6. ω = 78.74 rad/s

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