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 m0 → 1300 rpm110 kg

A flywheel of mass 110 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 1300 rpm. This takes 6 s. Ignoring friction, find the constant torque T needed.

m = 110 kgk = 0.3 mn1 = 0 rpmn2 = 1300 rpmt = 6 s
T = N·m
2.Easy
k = 0.15 m0 → 400 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 400 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.

m = 150 kgk = 0.15 mn1 = 0 rpmn2 = 400 rpmt = 30 s
T = N·m
3.Medium
11 kgaαM = 17 kgR = 0.1 m

An 11 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17 kg and radius 0.1 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 11 kgM = 17 kgR = 0.1 mg = 9.81 m/s²
α = rad/s²
4.Medium
6.5 kgaαM = 10 kgR = 0.45 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 1 m.

m = 6.5 kgM = 10 kgR = 0.45 mg = 9.81 m/s²h = 1 m
v = m/s
5.Hard
2 m/sω

A thin hoop of mass 17.5 kg rolls without slipping at 2 m/s. Find its rotational kinetic energy Erot.

m = 17.5 kgv = 2 m/sI = m·r²
Erot = J
6.Hard
0.85 m0.25 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 5 kgr1 = 0.85 mr2 = 0.25 mn1 = 25 rpm
n2 = rpm

Answer key

  1. 1. T = 224.6 N·m
  2. 2. T = 4.712 N·m
  3. 3. α = 55.34 rad/s²
  4. 4. v = 3.33 m/s
  5. 5. Erot = 35 J
  6. 6. n2 = 102.6 rpm

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