Final answer:
Rotational inertia depends on the distribution of mass relative to the axis of rotation. For a rod, the mass farther from the pivot contributes more to the inertia, explaining why a rod has greater inertia with mass at the end compared to a point mass at its midpoint.
Step-by-step explanation:
Understanding Rotational Inertia
The rotational inertia of a rod with an attached mass relates to how mass is distributed in relation to the axis of rotation. When the mass is closer to your hand or the pivot point, it has less rotational inertia compared to when the mass is farther away. This is because rotational inertia is calculated based on the distance each part of an object is from the axis of rotation, with those parts farther away contributing more due to the mass being distributed at a greater distance. According to the formula for a long rod spun around an end (I = ML²/3), we can see that the contribution to inertia increases with the square of the distance from the axis.
This concept is further reinforced by comparing the rotational inertia of a rod with the axis through one end to the rotational inertia if we only consider a point mass at the rod's center of mass. The distributed mass of the rod contributes more to the inertia because more mass is located beyond the midpoint of the rod, hence giving a higher value of ML²/3 as opposed to the point mass at L/2 which has an inertia of ML²/4.