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 m1000 → 2100 rpm30 kg

A flywheel of mass 30 kg with a radius of gyration of 0.3 m is accelerated uniformly from 1000 rpm to 2100 rpm. This takes 7 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.3 mn1 = 1000 rpmn2 = 2100 rpmt = 7 s
T = N·m
2.Easy
L = 2.7 mGOd = 0.4 mm = 3 kg

A uniform slender rod of mass 3 kg and length 2.7 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 = 3 kgL = 2.7 md = 0.4 m
IO = kg·m²
3.Medium
12.5 kgaαM = 17 kgR = 0.25 m

A 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 12.5 kgM = 17 kgR = 0.25 mg = 9.81 m/s²
a = m/s²
4.Medium
n = 500 rpmTb​ = 30 N·mI = 14.5 kg·m²

A flywheel with a moment of inertia of 14.5 kg·m² spins at 500 rpm. A brake applies a constant friction torque of 30 N·m. How long t does it take to stop?

I = 14.5 kg·m²n = 500 rpmTb = 30 N·m
t = s
5.Hard
θ = 20°as = 6 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 6 m down the slope?

θ = 20°I = m·r²g = 9.81 m/s²s = 6 m
t = s
6.Hard
disc: 38 kgring: 18 kgn1​ = 650 rpm

A uniform solid disc (mass 38 kg, radius 0.15 m) spins freely at 650 rpm about a vertical frictionless shaft. A thin ring of mass 18 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 = 38 kgMring = 18 kgR = 0.15 mn1 = 650 rpm
n2 = rpm

Answer key

  1. 1. T = 44.43 N·m
  2. 2. IO = 2.303 kg·m²
  3. 3. a = 5.839 m/s²
  4. 4. t = 25.31 s
  5. 5. t = 2.675 s
  6. 6. n2 = 333.8 rpm

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