Learning Goal:
To understand the concept of moment of inertia and how it depends on
mass, radius, and mass distribution.
In rigid-body rotational dynamics, the role analogous to the mass of a body
(when one is considering translational motion) is played by the body's
moment of inertia. For this reason, conceptual understanding of the motion
of a rigid body requires some understanding of moments of inertia. This
problem should help you develop such an understanding.
The moment of inertia of a body about some specified axis is $I = cmr^2$,
where c is a dimensionless constant, m is the mass of the body, and r is
the perpendicular distance from the axis of rotation. Therefore, if you have
two similarly shaped objects of the same size but with one twice as
massive as the other, the more massive object should have a moment of
inertia twice that of the less massive one. Furthermore, if you have two
similarly shaped objects of the same mass, but one has twice the size of
the other, the larger object should have a moment of inertia that is four
times that of the smaller one.
