The correct vector relation between linear velocity $ \vec{v} $ and angular velocity $ \vec{\omega } $ in rigid body dynamics is ( where $ \vec{r} $ is the position vector)
The vector relation between linear velocity $ \vec{v} $ and angular velocity $ \vec{\omega } $ in rigid body dynamics is $ \vec{v}=\vec{\omega }\times \vec{r} $ .
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.