Moment of inertia: A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses, it follows that A) I₁ = I₂. B) I₁ I₂. C) I₂ I₁.

Question

Moment of inertia: A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses, it follows that A) I₁ = I₂. B) I₁ > I₂. C) I₂ > I₁.

Quizplus · Accepted Answer

The moment of inertia depends on the distribution of mass relative to the axis of rotation. For $I_{\text{₁}}$, both masses are equidistant from the axis, leading to a certain moment of inertia. For $I_{\text{₂}}$, one mass is at the axis (contributing zero to the moment of inertia) and the other is twice as far compared to the first case, leading to a greater moment of inertia due to the square of the distance factor in the moment of inertia formula ($I = mr^2$).

Moment of Inertia: a Dumbbell-Shaped Object Is Composed by Two