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 flywheel of mass 30 kg has a radius of gyration of 0.6 m about its axis. It spins at 2000 rpm. Find its kinetic energy E_k in kJ.

M = 30 kgk = 0.6 mn = 2000 rpm

E_k = kJ

2.Easy

A uniform slender rod of mass 9.5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.15 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 9.5 kgL = 2.7 md = 1.15 m

I_O = kg·m²

3.Medium

A motor brings a flywheel with a moment of inertia of 2 kg·m² from rest up to 2800 rpm in 58 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 2 kg·m²n = 2800 rpmt = 58 s

P_avg = kW

4.Medium

A flywheel with a moment of inertia of 17 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 160 N·m. How long t does it take to stop?

I = 17 kg·m²n = 1400 rpmT_b = 160 N·m

t = s

5.Hard

A hollow sphere of mass 5 kg rolls without slipping at 7 m/s. Find its rotational kinetic energy E_rot.

m = 5 kgv = 7 m/sI = (2/3)·m·r²

E_rot = J

6.Hard

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 7 m along the slope.

θ = 40°s = 7 mI = m·r²g = 9.81 m/s²r = 0.2 m

ω = rad/s

Answer key

1. E_k = 236.9 kJ
2. I_O = 18.33 kg·m²
3. P_avg = 1.482 kW
4. t = 15.58 s
5. E_rot = 81.67 J
6. ω = 33.22 rad/s

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