Question

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 66 cm and is wound around the top at a spot where its radius is 1.4 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 +13 rad/s2. What is the final angular velocity of the top when the string is completely unwound?

Answer 1

Initial angular velocity of the top = ₁ = 0 rad/s (At rest)

Final angular velocity of the top = ₂

Angular acceleration of the top = = 13 rad/s²

Length of the string = L = 66 cm = 0.66 m

Radius of the top where the string is wound = R = 1.4 cm = 0.014 m

Angle through which the top rotates as the string is unwound = (radians)

= 47.14 rad

₂ = 35.01 rad/s

Final angular velocity of the top when the string is completely unwound = 35.01 rad/s