#28? 28. A top is a toy that is made to spin on its pointed end by Pulling on a
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#28? 28. 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 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 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?Explanation / Answer
The angular displacement can be calculated as follows:
theta = length / R
= 64 cm / 2.0 cm
= 32 rad
The final angular velocity of the top is,
w = [2(theta)(alpha)]1/2
= [(2)(32 rad)(12 rad/s2)]1/2
= 27.7 rad/s
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