Angular velocity -velocity conversion

AI Thread Summary
Angular velocity and linear velocity conversion can be confusing, particularly when applying the formula v = rw. The discussion centers on calculating angular velocity with respect to a reference point, specifically questioning if the formula v sin(θ)/r is applicable. The validity of v = rw is confirmed, as it holds true under uniform circular motion conditions. Additionally, the expression ω = (r x v)/r² is introduced to clarify the relationship between linear and angular velocities. Understanding these formulas is crucial for accurately converting between angular and linear velocities in various scenarios.
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angular velocity --velocity conversion

I am a bit confused about angular velocity --velocity conversion . I thought of a problem in my mind which is as follows

There is a particle moving with velocity v in certain direction as shown in the figure.and I want to calculate the angular velocity wrt the reference point. is it vsin@/r.

and also is v=rw valid in any condition for angular velocity --velocity conversion . please explain the validity of this formulae I didnt understand what this formulae( v=rw ) actually means
 

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You can use the expression ω=(rxv)/r^2.
 

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