Calculate the moment of inertia of each of the following uniform objects about t

Question

Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult TableMoments of Inertia of Various Bodies in the Textbook as needed.

a) A thin 3.10-

kg rod of length 80.0cm , about an axis perpendicular to it and passing through one end.

b) A thin 3.10-

kg rod of length 80.0cm , about an axis perpendicular to it and passing through its center.

c)A thin 3.10-kg

rod of length 80.0cm , about an axis parallel to the rod and passing through it.

d)A 3.50-

kg sphere 22.0cm in diameter, about an axis through its center, if the sphere is solid.

E) A 3.50-

kg sphere 22.0cm in diameter, about an axis through its center, if the sphere is a thin-walled hollow shell.

F) An 3.50-

kg cylinder, of length 27.0cm and diameter 24.0cm , about the central axis of the cylinder, if the cylinder is thin-walled and hollow.

G)An 3.50-

kg cylinder, of length 27.0cm and diameter 24.0cm , about the central axis of the cylinder, if the cylinder is solid

Explanation / Answer

a) I = mL^2 /3 = 3.10 x 0.80^2 /3 = 0.661 kg.m^2

b) I = mL^2 /12 = 0.165 kg.m2

c) I = 0

d) I = 2mr^2 /5 = 2 x 3.50 x 0.11^2 / 5 = 0.01694 kg.m2

e) I = 2mr^2 /3 = 0.0282 kg.m2

f) I = mr^2   = 3.50 x 0.12^2 = 0.0504

g) I = mr^2 /2 = 0.0252

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