Question

The rotational inertia of a pencil is greatest about an axis

A)along its length, where the lead is.
B)about its midpoint, like a propeller.
C)about its end, like a pendulum.

Answer 1

I = M L^2 description of moment of inertia I

Only (B) and (C) are useful because L is very small along the length

(C) has the largest momejnt:

I = M L^2 / 3 for a thin rod about one end

(I = M L^2 / 12 for a rod about its midpoint)