When calculating the moment of inertia of an object, can we treat all its mass as if it were concentrated at the center of mass of the object? Justify your answer.

The moment of inertia is equal to the product of the sum of the masses of the different particles and the square of the distance from the axis of rotation.

No, the mass of an object cannot be concentrated at the center of mass when calculating the moment of inertia.

This is because rotating an extended body about an axis is not the equivalent of rotating a point object of the same mass placed at the center of mass.

Moment of inertia refers to the resistance of change in rotational motion and these are not equal for an extended body and a particle of equal mass placed at the center of mass.

For example, the uniform disk has a moment of inertia as follows.

$l=\frac{1}{2}M{R}^2$

Here, M is mass of the disk, and R is the radius of the disk.

However, if this disk is replaced by a particle of mass M placed at the center of mass, the moment of inertia will be l = 0 because the distance from the particle to the center of mass will be zero.

Therefore, it cannot be treated all mass concentrated at the center of mass of the object while calculating the moment of inertia.