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 = 0.25 m100 → 700 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.25 m is accelerated uniformly from 100 rpm to 700 rpm. This takes 13 s. Ignoring friction, find the constant torque T needed.

m = 70 kgk = 0.25 mn1 = 100 rpmn2 = 700 rpmt = 13 s
T = N·m
2.Easy
k = 0.4 m0 → 1900 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 1900 rpm. The driving torque is a constant 250 N·m and friction can be ignored. How long t does this take?

m = 70 kgk = 0.4 mn1 = 0 rpmn2 = 1900 rpmT = 250 N·m
t = s
3.Medium
L = 1.6 mm = 13 kgα

A uniform slender rod of mass 13 kg and length 1.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 13 kgL = 1.6 mg = 9.81 m/s²
α = rad/s²
4.Medium
12 kgaαM = 14 kgR = 0.15 m

A 12 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 14 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 acceleration a of the block.

m = 12 kgM = 14 kgR = 0.15 mg = 9.81 m/s²
a = m/s²
5.Hard
θ = 10°a

A solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 10°I = (2/5)·m·r²g = 9.81 m/s²
a = m/s²
6.Hard
θ = 15°vs = 2.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 2.5 m along the slope.

θ = 15°s = 2.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.05 m
ω = rad/s

Answer key

  1. 1. T = 21.15 N·m
  2. 2. t = 8.914 s
  3. 3. α = 9.197 rad/s²
  4. 4. a = 6.196 m/s²
  5. 5. a = 1.217 m/s²
  6. 6. ω = 60.23 rad/s

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