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

A flywheel of mass 100 kg with a radius of gyration of 0.35 m is accelerated uniformly from 100 rpm to 300 rpm. This takes 8 s. Ignoring friction, find the constant torque T needed.

m = 100 kgk = 0.35 mn₁ = 100 rpmn₂ = 300 rpmt = 8 s

T = N·m

2.Easy

A flywheel of mass 140 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1400 rpm. This takes 25 s. Ignoring friction, find the constant torque T needed.

m = 140 kgk = 0.35 mn₁ = 0 rpmn₂ = 1400 rpmt = 25 s

T = N·m

3.Medium

A uniform slender rod of mass 5.5 kg and length 1.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 5.5 kgL = 1.2 mg = 9.81 m/s²

R = N

4.Medium

A 2 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9 kg and radius 0.3 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 = 2 kgM = 9 kgR = 0.3 mg = 9.81 m/s²

a = m/s²

5.Hard

A solid cylinder of mass 2 kg rolls without slipping at 8 m/s. What percentage p of its total kinetic energy is rotational?

m = 2 kgv = 8 m/sI = ½·m·r²

p = %

6.Hard

A solid cylinder of mass 13 kg rolls without slipping at 5 m/s. Find its rotational kinetic energy E_rot.

m = 13 kgv = 5 m/sI = ½·m·r²

E_rot = J

Answer key

1. T = 32.07 N·m
2. T = 100.6 N·m
3. R = 13.49 N
4. a = 3.018 m/s²
5. p = 33.33 %
6. E_rot = 81.25 J

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