How Do You Calculate the Final Angular Velocity of a Spinning Top?

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SUMMARY

The final angular velocity of a spinning top can be calculated using angular kinematics equations. Given that the initial angular velocity (ωinitial) is 0 rad/s and the angular acceleration (α) is 12 rad/s2, the top unwinds a string of length 64 cm, which corresponds to an angular distance (θ) that can be derived from the radius of 2.0 cm. The final angular velocity (ωfinal) can be determined using the equation ωfinal = ωinitial + α * t, where time (t) can be calculated from the distance unwound and the angular acceleration.

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Homework Statement



A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 64 cm and is wrapped around the top at a place where its radius is 2.0 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of 12 rad/s^2. What is the final angular velocity of the top when the string is completely unwound?

Homework Equations


Equations of angular kinematics


The Attempt at a Solution


I know that ωinitial is 0 rad/s, and that α is 12 rad/s^2, but I can't set up an equation.
 
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What angle will the top turn through while the string is unwinding (i.e. while the acceleration is occurring)? How might you relate angular velocity to angular acceleration and angular distance?
 

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