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 = 3 mGOd = 0.8 mm = 7 kg

A uniform slender rod of mass 7 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7 kgL = 3 md = 0.8 m
IO = kg·m²
2.Easy
k = 0.2 m300 → 2000 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.2 m is accelerated uniformly from 300 rpm to 2000 rpm. This takes 19 s. Ignoring friction, find the constant torque T needed.

m = 70 kgk = 0.2 mn1 = 300 rpmn2 = 2000 rpmt = 19 s
T = N·m
3.Medium
v = ?2.5 kgL = 1.3 mm = 9 kg

A uniform slender rod of mass 9 kg and length 1.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 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 = 9 kgL = 1.3 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
4.Medium
12.5 kgaαM = 20 kgR = 0.2 m

A 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 20 kg and radius 0.2 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 5 m.

m = 12.5 kgM = 20 kgR = 0.2 mg = 9.81 m/s²h = 5 m
v = m/s
5.Hard
240 m/s40 g1.68 mL = 1.7 m4.5 kgφ

A uniform slender rod of mass 4.5 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 240 m/s hits the rod 1.68 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 = 1.7 mm = 40 gv = 240 m/sd = 1.68 mg = 9.81 m/s²
φ = °
6.Hard
2 m/sω

A solid sphere of mass 0.5 kg rolls without slipping at 2 m/s. Find its rotational kinetic energy Erot.

m = 0.5 kgv = 2 m/sI = (2/5)·m·r²
Erot = J

Answer key

  1. 1. IO = 9.73 kg·m²
  2. 2. T = 26.24 N·m
  3. 3. v = 5.698 m/s
  4. 4. v = 7.382 m/s
  5. 5. φ = 76.46 °
  6. 6. Erot = 0.4 J

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