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The relation between angular velocity, position vector, and linear velocity of a particle moving in a circular path is:

1. $\vec v = \vec \omega \times \vec r$
2. $\vec v = \vec r \cdot \vec \omega$
3. $\vec v = \vec r \times \vec \omega$
4. $\vec v = \vec r\,\vec \omega$

Correct answer: $\vec v = \vec \omega \times \vec r$

Solution

For a particle in circular motion, the linear velocity is perpendicular to the radius vector and angular velocity vector. The correct vector relation is $\vec v = \vec \omega \times \vec r$. This gives the tangential direction correctly by the right-hand rule.

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