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Two particles 1 and 2 move with velociti...

Two particles `1 and 2` move with velocities `vec v_1` and `vec v_2` making the angles `theta_1 and theta_2` with the line joining them, respectively. Find angular velocity of ` relative to 1`.
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Text Solution

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Let us find the relative velocity between the particles perpendicular to the line joining them, the velocity of `1` relative to velocity of `2` is
`vec v_(12) = vec v_1 - vec v_2`
Then, `vec v_(12_y) =vec v_(1_y) - vec v_(2_y) = -v_1 sin theta_1 hat j - v_2 sin theta_2 hat j`
Hence, `omega_(12) = (|vec v_(12_y)|)/(l)`
Substituting `|vec v_(12_y)|`, we have
`omega_(12)= (v_1 sin theta_1 + v_2 sin theta_2)/(l)`.
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