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.

Solution 20DQ Numerically, moment of inertia of an object is equal to the summation of the product of mass of each point mass and the square of its distance from the axis of rotation. In other words, moment of inertia depends on the distribution of mass of the object. Suppose, an object has point masses m ,m , …., 1 loca2ed at distnnces r , r ,..., 1 2 r nrom the axis of rotation respectively. Therefore, the moment of inertia of the object is, I = m r 2+ m r 2 + ..... + m r 2 1 1 2 2 n n n I = m r 2 i=1 i i Therefore, I depends on the distance of each individual point mass from the rotation axis. The more the expanse of an object, more will be its moment of inertia since the distribution of mass of the object widens. Therefore, we cannot consider all the mass of the object to be concentrated at its center of mass.