A thin horizontal disc rotates about a vertical axis through its fixed centre O. Its angular momentum about points A and B, both in the plane of the disc, is Lₐ and Lᵦ, with OB = 2OA. Find Lₐ/Lᵦ. Image
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Question

A thin horizontal disc rotates about a vertical axis through its fixed centre O. Its angular momentum about points A and B, both in the plane of the disc, is Lₐ and Lᵦ, with OB = 2OA. Find Lₐ/Lᵦ. Image

Options

G1 Physics · Accepted Answer

Step 1: Angular momentum about a reference point P is L(P) = L(O) + (r_O − r_P) × P_total. Step 2: The disc rotates about a fixed centre O, so the total linear momentum of the whole disc P_total = Mv_cm = 0. Step 3: Consequently the second term vanishes for any reference point A or B, irrespective of their distances from O. Step 4: Lₐ = Lᵦ = L(O). Final answer: Lₐ/Lᵦ = 1 (Option C).