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Exam 3
PHY2425
Summer 2008
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Part II: Problem 1 (20 points)
Show all work.
A thin rod of length L has a nonuniform linear mass density
λ
= 20y
(kg/m) (for the coordinate system shown where the origin is at the
bottom end of the rod) as shown in the figure.
Report the final results
to each question in the table below.
Results
a.
Find the total mass, M, of the rod.
b.
Show that the moment of inertia of the rod about the zaxis (the axis
that passes through end A perpendicular to the rod) is
2
2
1
ML
I
A
=
2
2
1
ML
I
A
=
c.
Find the moment of inertia of the rod about an axis parallel to the z
axis that passes through the other end of the rod (the axis that passes
through end B perpendicular to the rod).
(Report the result as a
function of M and L)
d.
Find the moment of inertia of the rod about an axis parallel to the z
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 Spring '10
 Costello
 Biology, pH, Mass, Work

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