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 = 2.5 mGOd = 1.25 mm = 12 kg

A uniform slender rod of mass 12 kg and length 2.5 m rotates about an axis O perpendicular to the rod, 1.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 12 kgL = 2.5 md = 1.25 m
IO = kg·m²
2.Easy
k = 0.2 m900 → 1100 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.2 m is accelerated uniformly from 900 rpm to 1100 rpm. The driving torque is a constant 8.4 N·m and friction can be ignored. How long t does this take?

m = 120 kgk = 0.2 mn1 = 900 rpmn2 = 1100 rpmT = 8.4 N·m
t = s
3.Medium
v = ?3 kgL = 2.1 mm = 2 kg

A uniform slender rod of mass 2 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 2 kgL = 2.1 mmball = 3 kgg = 9.81 m/s²
v = m/s
4.Medium
15 kgaαM = 17.5 kgR = 0.1 m

A 15 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 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 = 15 kgM = 17.5 kgR = 0.1 mg = 9.81 m/s²
T = N
5.Hard
300 m/s20 g1.67 mL = 1.8 m7 kg

A uniform slender rod of mass 7 kg and length 1.8 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 300 m/s hits the rod 1.67 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 7 kgL = 1.8 mm = 20 gv = 300 m/sd = 1.67 m
ω = rad/s
6.Hard
2 m/sω

A hollow sphere of mass 12.5 kg rolls without slipping at 2 m/s. What percentage p of its total kinetic energy is rotational?

m = 12.5 kgv = 2 m/sI = (2/3)·m·r²
p = %

Answer key

  1. 1. IO = 25 kg·m²
  2. 2. t = 11.97 s
  3. 3. v = 6.704 m/s
  4. 4. T = 54.21 N
  5. 5. ω = 1.316 rad/s
  6. 6. p = 40 %

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