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 5.5 kg and length 0.6 m rotates about an axis O perpendicular to the rod, 0.1 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 5.5 kgL = 0.6 md = 0.1 m

I_O = kg·m²

2.Easy

A flywheel of mass 240 kg has a radius of gyration of 0.25 m about its axis. It spins at 2000 rpm. Find its kinetic energy E_k in kJ.

M = 240 kgk = 0.25 mn = 2000 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 7 kg and length 2.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 7 kgL = 2.5 mg = 9.81 m/s²

R = N

4.Medium

A motor brings a flywheel with a moment of inertia of 8 kg·m² from rest up to 2100 rpm in 36 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 8 kg·m²n = 2100 rpmt = 36 s

P_avg = kW

5.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3.5 m along the slope.

θ = 40°s = 3.5 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A hollow sphere of mass 3.5 kg rolls without slipping at 5.5 m/s. Find its rotational kinetic energy E_rot.

m = 3.5 kgv = 5.5 m/sI = (2/3)·m·r²

E_rot = J

Answer key

1. I_O = 0.22 kg·m²
2. E_k = 329 kJ
3. R = 17.17 N
4. P_avg = 5.373 kW
5. v = 5.146 m/s
6. E_rot = 35.29 J

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