How Does a Rod's Angular Velocity Relate to Its Movement in the X-Y Plane?

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The discussion revolves around calculating the angular velocity of a rod moving in the x-y plane, with one end at the origin and given velocities for both ends. The rod's length is 2m, and it makes a 30-degree angle with the x-axis. Key calculations involve determining the magnitude of angular velocity, the vertical component of velocity (v_y), and the velocity component of the center of mass perpendicular to the rod. The problem requires showing attempts at solving these calculations to understand the relationships between the rod's movement and its angular velocity. Understanding these concepts is crucial for solving similar physics problems.
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Homework Statement



A rod AB of length 2m moves in horizontal x-y plane. at any instant end A of rod is at origin and has velocity v_a =2i +v_y j. the other end B at the same instant is moving with velocity v_b = 2i +6j. the rod makes an angle of 30 degrees with the x-axis at this instant. find:

1. the magnitude of angular velocity of the rod.

2. value of v_y .

3. the component of velocity of cetre of mass in the direction perpendicular to the rod at given instant.
 
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