# Rank the moments of inertia of this object about the axes indicated.

Two identical uniform solid spheres are attached by a solid
uniform thin rod, as shown in the figure. The rod lies on a line
connecting the centers of mass of the two spheres. The axes A, B,
C, and D are in the plane of the page (which also contains the
centers of mass of the spheres and the rod), while axes E and F
(represented by black dots) are perpendicular to the page. (Figure
1). Rank the moments of inertia of this object about the axes
indicated. Rank from largest to
smallest. To rank items as equivalent, overlap them. Rank from largest to
smallest. To rank items as equivalent, overlap them. ABC

Rank the moments of inertia of this object about the axes
indicated. Rank from largest to smallest. To rank items as
equivalent, overlap them.
Moments of inertia depend on the masses and the perpendicular
distance from the axis of rotation. Mathematically it can be
expressed as

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I=Δmr2
The factor that effect the moment of inertia is the distance of the
center of mass of the objects in question to the axis of rotation,
so in this case

Axes C and F would represent the largest moments of inertia because
the center of mass of the rotating body is furthest from these two
axes of rotation. However, C and F would
have equal moments of inertia because they have equal distance
from the center of mass to their respective axis of rotation.

The next largest would be B because it is the next closest distance
from the center of mass.

A and E would come next in order because although they are exactly
between the two rotating masses, they still generate a moment of
inertia related to (y/2)^2

Finally, D has the lowest moment of inertia because the
perpendicular distance from the axis of rotation never exceeds
theradius of one of the balls. So in order from highest to
lowest:(C and F), B, (A and E), D

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