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 2.5 m rotates about an axis O perpendicular to the rod, 0.9 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 6.5 kgL = 2.5 md = 0.9 m

I_O = kg·m²

2.Easy

A flywheel of mass 150 kg has a radius of gyration of 0.55 m about its axis. It spins at 2700 rpm. Find its kinetic energy E_k in kJ.

M = 150 kgk = 0.55 mn = 2700 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 6.5 kg and length 1.8 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 = 6.5 kgL = 1.8 mg = 9.81 m/s²

ω = rad/s

4.Medium

A motor brings a flywheel with a moment of inertia of 39.5 kg·m² from rest up to 700 rpm in 40 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 39.5 kg·m²n = 700 rpmt = 40 s

P_avg = kW

5.Hard

A hollow sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?

θ = 15°I = (2/3)·m·r²g = 9.81 m/s²s = 4 m

t = s

6.Hard

A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?

θ = 40°I = (2/5)·m·r²g = 9.81 m/s²s = 4 m

t = s

Answer key

1. I_O = 8.65 kg·m²
2. E_k = 1814 kJ
3. ω = 4.044 rad/s
4. P_avg = 2.653 kW
5. t = 2.292 s
6. t = 1.333 s

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