Answer to Question #280092 in Physics for Faith

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 89 cm and is wrapped around the top at a place where its radius is 53.06 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 +19 rad/s^2. What is the final angular velocity of the top when the string is completely unwound?

Answer 1

Find the angle:

$$\phi=L/2R.$$

The angular velocity:

$$\omega=\sqrt{2\alpha\phi}=\sqrt{\frac {L\alpha}{R}}=5.65\text{ rad/s}.$$