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 8 kg and length 1.9 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 8 kgL = 1.9 md = 0.3 m

I_O = kg·m²

2.Easy

A uniform slender rod of mass 5.5 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 5.5 kgL = 2.2 md = 0.35 m

I_O = kg·m²

3.Medium

A flywheel with a moment of inertia of 30.5 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 150 N·m. How many revolutions N does the flywheel make before it stops?

I = 30.5 kg·m²n = 300 rpmT_b = 150 N·m

N = rev

4.Medium

A uniform slender rod of mass 17.5 kg and length 2.4 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration a_tip of the free end just after release.

m = 17.5 kgL = 2.4 mg = 9.81 m/s²

a_tip = m/s²

5.Hard

A solid sphere of mass 18.5 kg rolls without slipping at 3 m/s. Find its total kinetic energy E_k.

m = 18.5 kgv = 3 m/sI = (2/5)·m·r²

E_k = J

6.Hard

A solid cylinder rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 35°I = ½·m·r²g = 9.81 m/s²

μ_s =

Answer key

1. I_O = 3.127 kg·m²
2. I_O = 2.892 kg·m²
3. N = 15.97 rev
4. a_tip = 14.71 m/s²
5. E_k = 116.6 J
6. μ_s = 0.2334

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