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 12 kg and length 2.2 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 = 12 kgL = 2.2 md = 0.9 m

I_O = kg·m²

2.Easy

A flywheel is a uniform solid disc of mass 100 kg and radius 0.55 m. It spins at 700 rpm. Find its kinetic energy E_k in kJ.

M = 100 kgR = 0.55 mn = 700 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 1 kg and length 2.1 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 speed v of the free end as the rod swings through the vertical position.

m = 1 kgL = 2.1 mg = 9.81 m/s²

v = m/s

4.Medium

A motor delivers a torque of 1650 N·m at 2600 rpm. Find its power output P in kW.

T = 1650 N·mn = 2600 rpm

P = kW

5.Hard

A thin hoop of mass 20 kg rolls without slipping at 1.5 m/s. Find its rotational kinetic energy E_rot.

m = 20 kgv = 1.5 m/sI = m·r²

E_rot = J

6.Hard

A uniform solid disc (mass 9 kg, radius 0.15 m) spins freely at 150 rpm about a vertical frictionless shaft. A thin ring of mass 12 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n₂ in rpm.

M_disc = 9 kgM_ring = 12 kgR = 0.15 mn₁ = 150 rpm

n₂ = rpm

Answer key

1. I_O = 14.56 kg·m²
2. E_k = 40.64 kJ
3. v = 7.861 m/s
4. P = 449.2 kW
5. E_rot = 22.5 J
6. n₂ = 40.91 rpm

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