Combined translational and rotational motion of a rigid body

The velocity of any point P of a rigid body in rotation plus translation is [itex]\vec{}v[/itex]_p=[itex]\vec{}v[/itex]_COM+[itex]\vec{}v[/itex]_p,COM.
Now |[itex]\vec{}v[/itex]_COM|=v and [itex]\vec{}v[/itex]_p,COM =rω .
But v and rω are same thing as v=rω ,so velocity of the particle every time will be √2 v.Then what is the difference between [itex]\vec{}v[/itex]_COM and [itex]\vec{}v[/itex]_p,COM?

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