Two balls of masses m and 2 m are attached to the ends of a light rod of length L . The rod rotates with an angular speed ω about an axis passing through the centre of mass of system and perpendicular

Question

Two balls of masses m and 2 m are attached to the ends of a light rod of length L . The rod rotates with an angular speed ω about an axis passing through the centre of mass of system and perpendicular to the plane. Find the angular momentum of the system about the axis of rotation.

TestHub · Accepted Answer

Location of C M , X C M = 2 m × 0 + m × L 2 m + m = L 3 The velocity of ball, A w.r.t. the centre of mass C is V A = ω X C M = ω L 3 V B = ω L - X C M = 2 ω L 3 Thus, angular momentum of a system about C , L = 2 m v A X C M + m v B L - X C M = 2 m × ω L 3 × L 3 + m × 2 ω L 3 × 2 L 3 = 2 m ω L 2 3

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