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 180 kg has a radius of gyration of 0.5 m about its axis. It spins at 1800 rpm. Find its kinetic energy E_k in kJ.

M = 180 kgk = 0.5 mn = 1800 rpm

E_k = kJ

2.Easy

A flywheel of mass 210 kg has a radius of gyration of 0.35 m about its axis. It spins at 500 rpm. Find its kinetic energy E_k in kJ.

M = 210 kgk = 0.35 mn = 500 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 1 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 1 kgL = 2.1 mg = 9.81 m/s²

ω = rad/s

4.Medium

A uniform slender rod of mass 7.5 kg and length 1.7 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 7.5 kgL = 1.7 mg = 9.81 m/s²

v = m/s

5.Hard

A hollow sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9 m down the slope?

θ = 10°I = (2/3)·m·r²g = 9.81 m/s²s = 9 m

t = s

6.Hard

A thin hoop of mass 10 kg rolls without slipping at 9 m/s. What percentage p of its total kinetic energy is rotational?

m = 10 kgv = 9 m/sI = m·r²

p = %

Answer key

1. E_k = 799.4 kJ
2. E_k = 35.26 kJ
3. ω = 3.744 rad/s
4. v = 7.073 m/s
5. t = 4.197 s
6. p = 50 %

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