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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीConsider the following statements regarding the rotation of a rigid body about a fixed axis: (A) The total angular momentum vector \( \mathbf{L} \) is always parallel to the angular velocity vector \( \boldsymbol{\omega} \) for any arbitrary rigid body. (B) If the axis of rotation is an axis of symmetry of the body, then \( \mathbf{L} \) is parallel to \( \boldsymbol{\omega} \). (C) The component of angular momentum perpendicular to the fixed axis (\( \mathbf{L}_\perp \)) vanishes for a symmetric body rotating about its symmetry axis. (D) When the net external torque about the fixed axis is zero, the magnitude of total angular momentum is necessarily conserved even if the body is asymmetric. Which of the above statements are correct?
Correct answer · Option 4
(B) and (C) only
Explanation
\( \mathbf{L} \) is parallel to \( \boldsymbol{\omega} \) only when rotating about an axis of symmetry, making (B) correct and (A) incorrect. For symmetric bodies, pairs of particles cancel \( \mathbf{L}_\perp \), making (C) correct. (D) is incorrect because zero torque along the z-axis only conserves \( L_z \), while \( \mathbf{L}_\perp \) can vary if external torques perpendicular to the axis act.
