Problem.[]
A pendulum consists of a thin rod of length and mass m suspended from a pivot in the figure to the right. The bob is a cube of side L and mass M, attached to the rod so that the line of the rod extends through the center of the cube, from one corner to the diametrically opposite corner (dashed line).
(a) Locate the distance of the center of mass from the point of support.
(b) Find the moment of inertia I of the (entire) pendulum about the pivot point.
(Hint: obviously it is too hard to find the moment of inertia of a uniform cube about an arbitrary axis through its center of mass by integrating directly, so there must be some simple trick…)
(c) Write down the equation of motion in terms of I and any other relevant parameters.
(d) Find the frequency of small oscillations.