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
k = 0.3 m700 → 2500 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.3 m is accelerated uniformly from 700 rpm to 2500 rpm. The driving torque is a constant 300 N·m and friction can be ignored. How long t does this take?

m = 70 kgk = 0.3 mn1 = 700 rpmn2 = 2500 rpmT = 300 N·m
t = s
2.Easy
k = 0.3 m0 → 1300 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 1300 rpm. The driving torque is a constant 390 N·m and friction can be ignored. How long t does this take?

m = 160 kgk = 0.3 mn1 = 0 rpmn2 = 1300 rpmT = 390 N·m
t = s
3.Medium
n = 1500 rpmTb​ = 130 N·mI = 20.5 kg·m²

A flywheel with a moment of inertia of 20.5 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 130 N·m. How many revolutions N does the flywheel make before it stops?

I = 20.5 kg·m²n = 1500 rpmTb = 130 N·m
N = rev
4.Medium
L = 0.9 mm = 4 kgα

A uniform slender rod of mass 4 kg and length 0.9 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 = 4 kgL = 0.9 mg = 9.81 m/s²
atip = m/s²
5.Hard
9 m/sω

A solid cylinder of mass 2.5 kg rolls without slipping at 9 m/s. Find its rotational kinetic energy Erot.

m = 2.5 kgv = 9 m/sI = ½·m·r²
Erot = J
6.Hard
θ = 20°as = 2.5 m

A hollow sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2.5 m down the slope?

θ = 20°I = (2/3)·m·r²g = 9.81 m/s²s = 2.5 m
t = s

Answer key

  1. 1. t = 3.958 s
  2. 2. t = 5.027 s
  3. 3. N = 309.6 rev
  4. 4. atip = 14.71 m/s²
  5. 5. Erot = 50.63 J
  6. 6. t = 1.576 s

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