1.

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`. .

Answer» Angular velocity of `A` with respect to `O` is
`omega_(A O) = ((v_(A O))_|_)/(r_(A O))=(v)/(r) = omega`
Now, `omega_(A B) = ((v_(A B))_|_)/(r_(A B)) rArr v_(A B) = 2 v`
Since `v_(A B)` is perpendicular to `r_(A B) rArr (v_(A B)) _|_ = v_(A B) = 2 v , r_(A B) = 2 r`
`rArr omega_(A B) = ((v_(A B))_|_)/(r_(A B)) = (2 v)/(2 r) = omega`.


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