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 m500 → 1400 rpm130 kg

A flywheel of mass 130 kg with a radius of gyration of 0.3 m is accelerated uniformly from 500 rpm to 1400 rpm. This takes 20 s. Ignoring friction, find the constant torque T needed.

m = 130 kgk = 0.3 mn1 = 500 rpmn2 = 1400 rpmt = 20 s
T = N·m
2.Easy
Or = 0.05 mL = 1.2 m1.25 m1.5 kg10 kg

A pendulum is made of a uniform slender rod (1.5 kg, 1.2 m long) pivoted at its top end O, with a thin solid disc of mass 10 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1.5 kgL = 1.2 mmdisc = 10 kgr = 0.05 md = 1.25 m
IO = kg·m²
3.Medium
0 → 1600 rpmI = 40 kg·m²

A motor brings a flywheel with a moment of inertia of 40 kg·m² from rest up to 1600 rpm in 53 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 40 kg·m²n = 1600 rpmt = 53 s
Pavg = kW
4.Medium
0 → 3000 rpmI = 2 kg·m²

A motor brings a flywheel with a moment of inertia of 2 kg·m² from rest up to 3000 rpm in 52 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 2 kg·m²n = 3000 rpmt = 52 s
Pavg = kW
5.Hard
θ = 35°a

A thin hoop rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 35°I = m·r²g = 9.81 m/s²
μs =
6.Hard
100 m/s30 g0.59 mL = 0.6 m3.5 kg

A uniform slender rod of mass 3.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 100 m/s hits the rod 0.59 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 3.5 kgL = 0.6 mm = 30 gv = 100 m/sd = 0.59 m
ω = rad/s

Answer key

  1. 1. T = 55.13 N·m
  2. 2. IO = 16.36 kg·m²
  3. 3. Pavg = 10.59 kW
  4. 4. Pavg = 1.898 kW
  5. 5. μs = 0.3501
  6. 6. ω = 4.112 rad/s

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