A 6.00 kg mass is located at (2.00 m, 2.00 m, 2.00 m) and a 5.00 kg mass is located at (−1.0 m, 3.00 m, −2.00 m). The rotational inertia of this system of masses about the Y-axis, perpendicular to the Z-X plane, is A) 73 kg m². B) 66 kg m². C) 60 kg m². D) 55 kg m². E) 48 kg m².

Question

Quizplus · Accepted Answer

The rotational inertia (moment of inertia) $I$ about the Y-axis for a system of point masses is calculated using the formula $I = \sum m_i r_i^2$, where $m_i$ is the mass of the ith point mass and $r_i$ is the perpendicular distance of the ith mass from the axis of rotation. For the 6.00 kg mass, the distance from the Y-axis is $\sqrt{2^2 + 2^2} = \sqrt{8}$ m. For the 5.00 kg mass, the distance from the Y-axis is $\sqrt{(-1)^2 + (-2)^2} = \sqrt{5}$ m. Thus, the total rotational inertia is $I = 6(\sqrt{8})^2 + 5(\sqrt{5})^2 = 6(8) + 5(5) = 48 + 25 = 73$ kg m^2.

A 600 Kg Mass Is Located at (2