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 110 kg has a radius of gyration of 0.35 m about its axis. It spins at 1900 rpm. Find its kinetic energy E_k in kJ.

M = 110 kgk = 0.35 mn = 1900 rpm

E_k = kJ

2.Easy

A uniform slender rod of mass 4.5 kg and length 2.9 m rotates about an axis O perpendicular to the rod, 1.3 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 4.5 kgL = 2.9 md = 1.3 m

I_O = kg·m²

3.Medium

A uniform slender rod of mass 5.5 kg and length 2.3 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 = 5.5 kgL = 2.3 mg = 9.81 m/s²

a_tip = m/s²

4.Medium

A motor delivers a torque of 1540 N·m at 2000 rpm. Find its power output P in kW.

T = 1540 N·mn = 2000 rpm

P = kW

5.Hard

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 25°I = m·r²g = 9.81 m/s²

a = m/s²

6.Hard

A thin hoop starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 6 m along the slope.

θ = 30°s = 6 mI = m·r²g = 9.81 m/s²r = 0.2 m

ω = rad/s

Answer key

1. E_k = 266.7 kJ
2. I_O = 10.76 kg·m²
3. a_tip = 14.71 m/s²
4. P = 322.5 kW
5. a = 2.073 m/s²
6. ω = 27.12 rad/s

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