What is the effect of increasing mass on the moment of inertia of a solid object?

The moment of inertia of an object quantifies how difficult it is to change its rotational motion about an axis. It depends on both the mass of the object and how that mass is distributed with respect to the rotational axis.

As you increase the mass of a solid object while keeping the shape and distribution of that mass constant, the moment of inertia necessarily increases. This is because moment of inertia is mathematically defined as the sum of the products of each mass element and the square of its distance from the axis of rotation. Thus, with a larger total mass, the sum of these products becomes larger, leading to a higher moment of inertia.

Additionally, if the mass were distributed farther from the axis, the moment of inertia would increase even more dramatically due to the squared term in its definition. The increase in mass directly contributes to a greater resistance to rotational acceleration, confirming that the moment of inertia increases with mass. Therefore, the correct choice is that the moment of inertia increases with increasing mass.