Question

A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod, whose masses are each M and whose centers are separated by L. The spheres have radius R. If the sphere radius R is not negligible compared to the length L, what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center?


A. 2MR2


B. 2ML2


C. 2ML2 + 2MR2


D. (1/2) ML2


E. (1/2) ML2 + 2MR2

Answer 1

Using the parallel axes theorem gives

$$I=2\left(\frac{2mR^2}{2} +m\frac{L^2}{2^2}\right)=\frac{mL^2}{2}+2mR^2$$

Answer: E