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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीRefer to the given figure depicting a particle \( P \) of a rigid body rotating about the fixed \( z \)-axis with angular velocity vector \( \vec{\omega} \). Point \( C \) is the centre of the circular path of radius \( r_\perp \) in the plane perpendicular to the axis, and \( O \) is the origin on the rotation axis. Which of the following vector expressions correctly represents the linear velocity \( \vec{v} \) of particle \( P \)?
Correct answer · Option 4
\( \vec{v} = \vec{\omega} \times \vec{r} = \vec{\omega} \times \vec{CP} \)
Explanation
Linear velocity is given by \( \vec{v} = \vec{\omega} \times \vec{r} \). Since \( \vec{r} = \vec{OC} + \vec{CP} \) and \( \vec{\omega} \times \vec{OC} = 0 \), we have \( \vec{v} = \vec{\omega} \times \vec{CP} \).
