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 = 0.1 m0 → 1600 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1600 rpm. This takes 9 s. Ignoring friction, find the constant torque T needed.

m = 180 kgk = 0.1 mn1 = 0 rpmn2 = 1600 rpmt = 9 s
T = N·m
2.Easy
Or = 0.15 mL = 0.4 m0.55 m3 kg1 kg

A pendulum is made of a uniform slender rod (3 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3 kgL = 0.4 mmsphere = 1 kgr = 0.15 md = 0.55 m
IO = kg·m²
3.Medium
n = 2300 rpmTb​ = 35 N·mI = 4.5 kg·m²

A flywheel with a moment of inertia of 4.5 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 35 N·m. How many revolutions N does the flywheel make before it stops?

I = 4.5 kg·m²n = 2300 rpmTb = 35 N·m
N = rev
4.Medium
4.5 kgaαM = 11 kgR = 0.5 m

A 4.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 11 kg and radius 0.5 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 = 11 kgR = 0.5 mg = 9.81 m/s²
T = N
5.Hard
θ = 20°as = 10 m

A thin hoop 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 10 m down the slope?

θ = 20°I = m·r²g = 9.81 m/s²s = 10 m
t = s
6.Hard
disc: 34 kgring: 15 kgn1​ = 400 rpm

A uniform solid disc (mass 34 kg, radius 0.1 m) spins freely at 400 rpm about a vertical frictionless shaft. A thin ring of mass 15 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 = 34 kgMring = 15 kgR = 0.1 mn1 = 400 rpm
ΔE = J

Answer key

  1. 1. T = 33.51 N·m
  2. 2. IO = 0.4715 kg·m²
  3. 3. N = 593.5 rev
  4. 4. T = 24.28 N
  5. 5. t = 3.453 s
  6. 6. ΔE = 69.91 J

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