The thin semi-circular part ABC has mass m 1 and diameter AOC has mass m 2 . Here, axis passes through mid-point of diameter and the axis is perpendicular to plane ABC . Here, A O = O C = R . The mome

Question

The thin semi-circular part ABC has mass m 1 and diameter AOC has mass m 2 . Here, axis passes through mid-point of diameter and the axis is perpendicular to plane ABC . Here, A O = O C = R . The moment of inertia of this composite system about the axis is

TestHub · Accepted Answer

According to the diagram, I = I A B C + I A O C = m 1 R 2 + m 2 A C 2 12 = m 1 R 2 + m 2 2 R 2 12 ∵ O A = O C = R ∴ A C = 2 R = R 2 m 1 + m 2 4 R 2 12 I = m 1 R 2 + m 2 R 2 3

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