Question

How does the mass of an object affect the moment of inertia?

Answer 1

Hint: The body's moment of inertia is the object's additional property. It is possible to calculate the moment of body inertia using the formula:
$I=\sum{{{m}_{i}}{{r}_{i}}^{2}}$
A rigid body's moment of inertia, otherwise referred to as the mass moment of inertia, angular mass or rotational inertia, is a quantity that determines the torque required for a desired angular acceleration around a rotational axis.

Complete answer:
1.An object's tendency to resist alterations in its state of motion varies with mass. Mass is the amount that depends exclusively on an object's inertia.
2.The more inertia an object possesses, the more mass it has.
3.Rotational inertia is also known as the moment of inertia. Its rotational analogue is known as rotational inertia when masses are in linear movement.
4.The moment of inertia provides the connection to rotational motion dynamics. It is possible to calculate the moment of inertia with respect to the rotation axis of the particles.
In its state of motion, a more massive object has a greater tendency to resist changes. Considering the object consists of $\mathrm{n}$ number of particles, the distance of each particle is $\mathrm{r}$ from its axis of rotation. The formula of the moment of inertia can be given as:
$I=\sum m_{n} r_{n}^{2}$
Where, $m_{n}$ is the mass of each particle of the object and $r_{n}$ is the distance of the particle from the axis of rotation. The distance of each particle from the axis of rotation is dependent on the shape and size of the object. Therefore,
$I \propto m$
$I \propto r^{2}$
Thus, the moment of inertia of the object depends on the mass, axis of rotation and shape and size of the body.

Note:
Thus, in other terms, the moment of inertia is known as the particle's mass distribution with respect to the axis of rotation. .The distribution of the particle from the rotation axis is also dependent on the object's shape and size. Thus the moment of the object's inertia depends on the body's mass, rotation axis, and shape and size.