A uniform thin rod of length 1.20m and mass 2.0kg can be pivoted about any axis perpendicular to the rod and located along the rod’s length.
Engineers wish to mount the rod on a pivot so that its rotational inertia about the pivot is exactly twice the value it would have if the pivot were located at the rod’s center of mass.
Respond to prompts (a)–(c).
(a) Derive an algebraic expression for the rotational inertia of the rod about an arbitrary pivot that lies a distance d from its center of mass.
(b) Using your expression, determine the required distance d that results in a rotational inertia equal to twice the rotational inertia about the center of mass.
(c) State whether there are two distinct pivot points on the rod that satisfy this requirement and, if so, specify their locations relative to the center of mass.