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 4 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 4 kgL = 2.3 md = 0.5 m

I_O = kg·m²

2.Easy

A uniform slender rod of mass 3 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 = 3 kgL = 2 md = 0.2 m

I_O = kg·m²

3.Medium

A 15 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 13 kg and radius 0.1 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 15 kgM = 13 kgR = 0.1 mg = 9.81 m/s²

T = N

4.Medium

A flywheel with a moment of inertia of 17.5 kg·m² spins at 2700 rpm. A brake applies a constant friction torque of 120 N·m. How long t does it take to stop?

I = 17.5 kg·m²n = 2700 rpmT_b = 120 N·m

t = s

5.Hard

A solid cylinder of mass 8 kg rolls without slipping at 3.5 m/s. Find its rotational kinetic energy E_rot.

m = 8 kgv = 3.5 m/sI = ½·m·r²

E_rot = J

6.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8 m along the slope.

θ = 15°s = 8 mI = ½·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. I_O = 2.763 kg·m²
2. I_O = 1.12 kg·m²
3. T = 44.49 N
4. t = 41.23 s
5. E_rot = 24.5 J
6. v = 5.204 m/s

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