A thin horizontal disc rotates about a vertical axis passing through its fixed centre O. Its angular momentum is L_A and L_B when computed about points A and B respectively, where OB=2× OA. The value of (L_A)/(L_B) is:

Solution & Explanation

Principle: about a general point, L = L_orbital + L_spin = (r_cm × P_cm) + I_cm·ω. Here the disc spins about its own fixed centre O, so its centre of mass does not move — its linear momentum P_cm = 0. Therefore the orbital term r × P_cm vanishes for ANY reference point, whether A or B. What remains is only the spin angular momentum about the centre, I_cm·ω, which is the same regardless of where the reference point sits. So L_A = I_cm·ω and L_B = I_cm·ω are equal. Hence L_A/L_B = 1, independent of the fact that OB = 2·OA. Key trap: the distances OA, OB tempt you to scale L with r, but with a non-translating centre the position of the reference point is irrelevant — answer (C), 1.