Finding resultant velocity from angular acceleration

AI Thread Summary
To find the resultant velocity of the rope when it leaves Michael's hand, one must first convert angular acceleration to angular velocity. The angular acceleration of 2.00 rad/s² can be integrated over the 3 seconds to determine the angular velocity. Additionally, the linear velocity of Michael running at 4.00 m/s² must be considered, as it contributes to the rope's final velocity. The relationship between angular velocity and linear velocity can be expressed using the formula v = rω, where r is the length of the rope segment. Understanding these relationships and applying the appropriate kinematic equations will yield the resultant velocity of the rope.
Michael Fox
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Homework Statement


Michael starts spinning the rope at a rate of 2.00 rad/s^2 while he starts running towards the target at 4.00m/s^2. This distance betweens Michael's elbow and the end of the rope form a straight 1.2m segment. If Michael takes 3 seconds before he launches the rope at the target, what is the resultant velocity of the rope when it leaves Michael's hand.

Homework Equations


at= (v2-v1)/2 (i think)
at=ra (at= linear acceleration, a = angular acceleration)

The Attempt at a Solution


I believe to solve I would have to convert angular acceleration to angular velocity but I cannot figure out how to do that. Any help clarifying or a diagram would be huge. Thank you for reading
 
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What is the relation between angular acceleration and angular velocity? What is the relation between angular velocity and velocity?
 
You probably have some kinematic equations that can handle that "transformation".
 

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