Two point masses of 5.0 kg and 15.0 kg, separated by 2.0 m, are spinning about their center of mass. The moment of inertia of the system is A) 5.0 kg^.m². B) 10 kg^.m². C) 16 kg^.m². D) 20 kg^.m².

Question

Quizplus · Accepted Answer

The moment of inertia (I) for a system of point masses can be calculated using the formula $I = \sum m_i r_i^2$, where $m_i$ is the mass of each point and $r_i$ is the distance of each point from the axis of rotation (in this case, the center of mass). The center of mass of a system of two masses, $m_1$ and $m_2$, separated by a distance $d$, is located at a distance $r_1 = \frac{m_2}{m_1 + m_2}d$ from $m_1$ and $r_2 = \frac{m_1}{m_1 + m_2}d$ from $m_2$. For the given masses of 5.0 kg and 15.0 kg separated by 2.0 m, the distances from the center of mass to each mass are $r_1 = \frac{15}{20} \times 2 = 1.5$ m and $r_2 = \frac{5}{20} \times 2 = 0.5$ m. Thus, the moment of inertia is $I = (5.0 \times 1.5^2) + (15.0 \times 0.5^2) = 11.25 + 3.75 = 15$ kg·m². However, due to the options provided not matching the calculated value exactly and assuming a possible calculation or typographical error in the question or answer choices, the closest correct option based on standard calculation methods is not listed. Given the context, the correct methodology leads to a result that should be reconsidered in light of the provided options.

Two Point Masses of 5