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 uniform slender rod of mass 12 kg and length 0.8 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 12 kgL = 0.8 md = 0.2 m

I_O = kg·m²

2.Easy

A flywheel of mass 160 kg has a radius of gyration of 0.2 m about its axis. It spins at 1700 rpm. Find its kinetic energy E_k in kJ.

M = 160 kgk = 0.2 mn = 1700 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 39.5 kg·m² spins at 2700 rpm. A brake applies a constant friction torque of 25 N·m. How long t does it take to stop?

I = 39.5 kg·m²n = 2700 rpmT_b = 25 N·m

t = s

4.Medium

A uniform slender rod of mass 6 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 = 6 kgL = 1.7 mg = 9.81 m/s²

v = m/s

5.Hard

A solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 40°I = ½·m·r²g = 9.81 m/s²

a = m/s²

6.Hard

A thin hoop of mass 19.5 kg rolls without slipping at 5.5 m/s. Find its rotational kinetic energy E_rot.

m = 19.5 kgv = 5.5 m/sI = m·r²

E_rot = J

Answer key

1. I_O = 1.12 kg·m²
2. E_k = 101.4 kJ
3. t = 446.7 s
4. v = 7.073 m/s
5. a = 4.204 m/s²
6. E_rot = 294.9 J

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