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 = 1 mGOd = 0.1 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 1 m rotates about an axis O perpendicular to the rod, 0.1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5.5 kgL = 1 md = 0.1 m
IO = kg·m²
2.Easy
k = 0.4 m0 → 800 rpm190 kg

A flywheel of mass 190 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 800 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.4 mn1 = 0 rpmn2 = 800 rpmt = 28 s
T = N·m
3.Medium
0 → 400 rpmI = 3.5 kg·m²

A motor brings a flywheel with a moment of inertia of 3.5 kg·m² from rest up to 400 rpm in 29 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 3.5 kg·m²n = 400 rpmt = 29 s
Pavg = kW
4.Medium
n = 1600 rpmTb​ = 105 N·mI = 40 kg·m²

A flywheel with a moment of inertia of 40 kg·m² spins at 1600 rpm. A brake applies a constant friction torque of 105 N·m. How many revolutions N does the flywheel make before it stops?

I = 40 kg·m²n = 1600 rpmTb = 105 N·m
N = rev
5.Hard
disc: 16 kgring: 9 kgn1​ = 400 rpm

A uniform solid disc (mass 16 kg, radius 0.45 m) spins freely at 400 rpm about a vertical frictionless shaft. A thin ring of mass 9 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 = 16 kgMring = 9 kgR = 0.45 mn1 = 400 rpm
ΔE = J
6.Hard
θ = 25°vs = 9 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 9 m along the slope.

θ = 25°s = 9 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 0.5133 kg·m²
  2. 2. T = 90.96 N·m
  3. 3. Pavg = 0.1059 kW
  4. 4. N = 851.1 rev
  5. 5. ΔE = 752.4 J
  6. 6. v = 6.691 m/s

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