Question

The size of an object parallel to the axis of rotation does not enter into the calculation of its moment of inertia. Why?

Answer 1

Moment of Inertia or Rotational Inertia is a property of any object which can be rotated. It is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis.

Rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics. Indeed, the rotational inertia of an object depends on its mass. It also depends on the distribution of that mass relative to the axis of rotation. When a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system. Intuitively, this is because the mass is now carrying more momentum with it around the circle and because the momentum vector is changing more quickly. Both of these effects depend on the distance from the axis.

Rotational inertia is given by symbol I. For a single body such as an object of mass M rotating at radius R from the axis of roatation, the moment of inertia I is

I = MR^2

So, the size of the object is not considered in the calculation of the moment of Inertia.