Calculating Rotation Angle: Mass & Cord Problem Explained

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A block of mass 459 g is attached to a cord of mass 3.3 g, rotating with constant angular speed on a frictionless table. The discussion centers on calculating the angle through which the block rotates while a transverse wave travels along the cord. Initial calculations involved using the relationships v = omega/r and v = sqrt(T/mu), leading to a radius of 0.084 m. The tension in the cord was expressed as T = (0.45 kg + 0.0032 kg * r) * (r * omega^2). The user struggles to derive the angle d(theta) from the angular speed omega, indicating a need for further guidance on the calculations.
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so there's a blcok of mass 459 g attached to one end of a cord of mass 3.3 g and the other end of the cord is attached to a fixed point. The block rotates with constant angular spd in a circle on a horizontal frictionless table. Through what angle does the block rotate in teh time that a transverse wave takes to travel along the string from the center of the circle to the block. I don't know how to start this at all.

EDIT: Nvm I got it
 
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I don't get it. I've tried using v = omega/r and v = sqrt(T/mu). I did calculate the radius to be .084 m at one point by substituting some equations and solving a cubic with r. I used T = (.45 kg + .0032kg*r)*(r*omega^2). I then combined that equation into the v = sqrt(T/mu) to get the value of r = .084. But I can't figure out where to go from there to get d(theta). I know omega = d(theta)/dt, but that's all I've got.
 
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