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 = 0.4 mn = 2300 rpm190 kg

A flywheel of mass 190 kg has a radius of gyration of 0.4 m about its axis. It spins at 2300 rpm. Find its kinetic energy Ek in kJ.

M = 190 kgk = 0.4 mn = 2300 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.9 m1.1 m2.5 kg4 kg

A pendulum is made of a uniform slender rod (2.5 kg, 0.9 m long) pivoted at its top end O, with a thin solid disc of mass 4 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 0.9 mmdisc = 4 kgr = 0.2 md = 1.1 m
IO = kg·m²
3.Medium
4.5 kgaαM = 13 kgR = 0.15 m

A 4.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 13 kg and radius 0.15 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 4.5 kgM = 13 kgR = 0.15 mg = 9.81 m/s²
T = N
4.Medium
n = 400 rpmTb​ = 140 N·mI = 26 kg·m²

A flywheel with a moment of inertia of 26 kg·m² spins at 400 rpm. A brake applies a constant friction torque of 140 N·m. How long t does it take to stop?

I = 26 kg·m²n = 400 rpmTb = 140 N·m
t = s
5.Hard
3 m/sω

A hollow sphere of mass 16.5 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 16.5 kgv = 3 m/sI = (2/3)·m·r²
p = %
6.Hard
disc: 30 kgring: 8 kgn1​ = 450 rpm

A uniform solid disc (mass 30 kg, radius 0.4 m) spins freely at 450 rpm about a vertical frictionless shaft. A thin ring of mass 8 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 30 kgMring = 8 kgR = 0.4 mn1 = 450 rpm
n2 = rpm

Answer key

  1. 1. Ek = 881.8 kJ
  2. 2. IO = 5.595 kg·m²
  3. 3. T = 26.09 N
  4. 4. t = 7.779 s
  5. 5. p = 40 %
  6. 6. n2 = 293.5 rpm

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