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Linear Momentum in Rotational motion

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It is known that for a mass (m) that moves with velocity (v) the linear momentum is (m)x(v). Now, assume we have a rod of mass (m) and radius (R) that
rotates with constant angular velocity (w). Also, isolate only half of the cycle (rotation for 180 degrees). What is the linear momentum of the rod on y-axis? Is it a function of sin(th) where (th) is the angle of rotation? (assume x,y axes and the rod begins rotation when it is on y axis and finishes on the other end of axis y). Thank you.

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