Particles `A and B` move with constant and equal speeds in a circle as shown in (Fig. 5.164). Find the angular velocity of the particle A with respect to `B`, if the angular velocity of particle `A w.r.t. O` is `omega`.
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Explanation

Angular velocity of `A` with respect to `O` is
`omega_(A C) = ((v_(A O))_|_)/(r_(A O)) = (v)/( r)= omega`
`:. omega_(A B) = ((v_(A B))_|_)/(r_(A B))= (v)/(2 r)=(omega)/(2)`
and `omega_(A C) = ((v_(A C))_|_)/(r_(A C)) = (v)/(3 r) = (omega)/(3)`.