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 140 kg has a radius of gyration of 0.45 m about its axis. It spins at 2000 rpm. Find its kinetic energy E_k in kJ.

M = 140 kgk = 0.45 mn = 2000 rpm

E_k = kJ

2.Easy

A flywheel of mass 100 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1700 rpm. The driving torque is a constant 42 N·m and friction can be ignored. How long t does this take?

m = 100 kgk = 0.2 mn₁ = 0 rpmn₂ = 1700 rpmT = 42 N·m

t = s

3.Medium

A uniform slender rod of mass 1 kg and length 3 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 = 1 kgL = 3 mg = 9.81 m/s²

α = rad/s²

4.Medium

A uniform slender rod of mass 3.5 kg and length 3 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 = 3.5 kgL = 3 mg = 9.81 m/s²

α = rad/s²

5.Hard

A solid sphere of mass 8.5 kg rolls without slipping at 4 m/s. What percentage p of its total kinetic energy is rotational?

m = 8.5 kgv = 4 m/sI = (2/5)·m·r²

p = %

6.Hard

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. Find its speed v after it has rolled 7.5 m along the slope.

θ = 15°s = 7.5 mI = (2/5)·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. E_k = 621.8 kJ
2. t = 16.95 s
3. α = 4.905 rad/s²
4. α = 4.905 rad/s²
5. p = 28.57 %
6. v = 5.216 m/s

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