1. A top is a toy that is made to spin on its pointed end by pulling on the string wrapped around the body of the top. The string has a length of 64cm and is wound around the top at a spot 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 thes stirng, theryb undwinding it and givig the top and an angular acceleration of +12 rad/s^2. What is the final angular velocity of the top when the string is completely unwound? 2. Relevant equations [tex]\alpha[/tex] = [tex]\omega[/tex]/t [tex]\omega[/tex] = [tex]\theta[/tex] /t Circumfrence: [tex]\pi[/tex]r^2 3. The attempt at a solution First I found that the circle's circumference is 4[tex]\pi[/tex]. Then I divided 64cm/4[tex]\pi[/tex] to find that the rope wraps around 5.09 times. I know that 360 degrees is equal to 2[tex]\pi[/tex]radians, so 5.09 x 360 degrees = 1833.5 degrees. Then 1833.5 degrees x ([tex]\pi[/tex] radian / 180 degrees ) = 10.2 radians Therefore I know the angular displacement, which is from 0 to 10.2 radians Then I am stumped on how to find the time from that. I know that I can find the final angular velocity by using the time in the angular acceleration formula. Because Angular acceleration is equal to the final velocity / time. I know this because the initial velocity of the top was zero. In short I can't figure out how to find the time.