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 = 1.7 mGOd = 0.5 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.7 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 2.5 kgL = 1.7 md = 0.5 m
IO = kg·m²
2.Easy
k = 0.4 m0 → 500 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 500 rpm. The driving torque is a constant 96 N·m and friction can be ignored. How long t does this take?

m = 80 kgk = 0.4 mn1 = 0 rpmn2 = 500 rpmT = 96 N·m
t = s
3.Medium
n = 3000 rpmTb​ = 85 N·mI = 28.5 kg·m²

A flywheel with a moment of inertia of 28.5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 85 N·m. How long t does it take to stop?

I = 28.5 kg·m²n = 3000 rpmTb = 85 N·m
t = s
4.Medium
L = 2.1 mm = 11 kgα

A uniform slender rod of mass 11 kg and length 2.1 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 = 11 kgL = 2.1 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 40°a

A thin hoop rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 40°I = m·r²g = 9.81 m/s²
a = m/s²
6.Hard
0.75 m0.25 mn1​ = 35 rpm

A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.75 m from the axis. The person and turntable alone have a moment of inertia of 2.5 kg·m² about the axis. They turn at 35 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 2.5 kg·m²m = 2 × 5.5 kgr1 = 0.75 mr2 = 0.25 mn1 = 35 rpm
n2 = rpm

Answer key

  1. 1. IO = 1.227 kg·m²
  2. 2. t = 6.981 s
  3. 3. t = 105.3 s
  4. 4. atip = 14.71 m/s²
  5. 5. a = 3.153 m/s²
  6. 6. n2 = 95.39 rpm

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