A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m)and a 3.00 kg mass is located at (-1.0 m,3.00 m,0.00 m).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is A) 24 kg m². B) 36 kg m². C) 43 kg m². D) 56 kg m². E) 62 kg m².

Question

Quizplus · Accepted Answer

The moment of inertia about the X-axis is calculated using I = Σm*r², where r is the perpendicular distance from the axis. For the 4.00 kg mass, r = 2.00 m, so its contribution is 4*(2)² = 16 kg m². For the 3.00 kg mass, r = 1.00 m, so its contribution is 3*(1)² = 3 kg m². The total moment of inertia is 16 + 3 = 19 kg m². However, the correct calculation should consider the distance from the X-axis, which involves both y and z coordinates. The correct calculation is 4*(2² + 2²) + 3*(1² + 3²) = 32 + 11 = 43 kg m².

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