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 6.5 kg and length 0.6 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 = 6.5 kgL = 0.6 md = 0.2 m

I_O = kg·m²

2.Easy

A uniform slender rod of mass 9 kg and length 2 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 = 9 kgL = 2 md = 0.2 m

I_O = kg·m²

3.Medium

A uniform slender rod of mass 10 kg and length 1 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 = 10 kgL = 1 mg = 9.81 m/s²

a_tip = m/s²

4.Medium

A motor brings a flywheel with a moment of inertia of 18.5 kg·m² from rest up to 900 rpm in 4 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 18.5 kg·m²n = 900 rpmt = 4 s

P_avg = kW

5.Hard

A hollow sphere of mass 16.5 kg rolls without slipping at 3 m/s. Find its total kinetic energy E_k.

m = 16.5 kgv = 3 m/sI = (2/3)·m·r²

E_k = J

6.Hard

A hollow sphere 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 = (2/3)·m·r²g = 9.81 m/s²

μ_s =

Answer key

1. I_O = 0.455 kg·m²
2. I_O = 3.36 kg·m²
3. a_tip = 14.71 m/s²
4. P_avg = 20.54 kW
5. E_k = 123.8 J
6. μ_s = 0.2801

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