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 10 kg and length 2.5 m rotates about an axis O perpendicular to the rod, 1 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 10 kgL = 2.5 md = 1 m

I_O = kg·m²

2.Easy

A flywheel of mass 80 kg has a radius of gyration of 0.35 m about its axis. It spins at 2900 rpm. Find its kinetic energy E_k in kJ.

M = 80 kgk = 0.35 mn = 2900 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 1.5 kg and length 0.7 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 = 1.5 kgL = 0.7 mg = 9.81 m/s²

α = rad/s²

4.Medium

A flywheel with a moment of inertia of 10.5 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 150 N·m. How many revolutions N does the flywheel make before it stops?

I = 10.5 kg·m²n = 1900 rpmT_b = 150 N·m

N = rev

5.Hard

A hollow sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 15°I = (2/3)·m·r²g = 9.81 m/s²

μ_s =

6.Hard

A solid cylinder of mass 5.5 kg rolls without slipping at 8 m/s. Find its rotational kinetic energy E_rot.

m = 5.5 kgv = 8 m/sI = ½·m·r²

E_rot = J

Answer key

1. I_O = 15.21 kg·m²
2. E_k = 451.9 kJ
3. α = 21.02 rad/s²
4. N = 220.5 rev
5. μ_s = 0.1072
6. E_rot = 88 J

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