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 = 0.8 mGOd = 0.4 mm = 11.5 kg

A uniform slender rod of mass 11.5 kg and length 0.8 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11.5 kgL = 0.8 md = 0.4 m
IO = kg·m²
2.Easy
k = 0.35 m400 → 600 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.35 m is accelerated uniformly from 400 rpm to 600 rpm. The driving torque is a constant 14 N·m and friction can be ignored. How long t does this take?

m = 160 kgk = 0.35 mn1 = 400 rpmn2 = 600 rpmT = 14 N·m
t = s
3.Medium
0 → 2100 rpmI = 2 kg·m²

A motor brings a flywheel with a moment of inertia of 2 kg·m² from rest up to 2100 rpm in 52 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 2 kg·m²n = 2100 rpmt = 52 s
Pavg = kW
4.Medium
n = 2100 rpmTb​ = 110 N·mI = 25.5 kg·m²

A flywheel with a moment of inertia of 25.5 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 110 N·m. How many revolutions N does the flywheel make before it stops?

I = 25.5 kg·m²n = 2100 rpmTb = 110 N·m
N = rev
5.Hard
θ = 35°vs = 4.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 4.5 m along the slope.

θ = 35°s = 4.5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
disc: 21 kgring: 19 kgn1​ = 1100 rpm

A uniform solid disc (mass 21 kg, radius 0.5 m) spins freely at 1100 rpm about a vertical frictionless shaft. A thin ring of mass 19 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 21 kgMring = 19 kgR = 0.5 mn1 = 1100 rpm
ΔE = J

Answer key

  1. 1. IO = 2.453 kg·m²
  2. 2. t = 29.32 s
  3. 3. Pavg = 0.93 kW
  4. 4. N = 892.1 rev
  5. 5. v = 6.014 m/s
  6. 6. ΔE = 11217 J

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