A yoyo with an axle diameter of 1.00 cm has a 90.0cm length of string wrapped around it many times in such a way that the string completely covers the surface of its axle, but there are no double layers of string. The outermost portion of the yoyo is 5.00 cm from the center of the axle.
(a) If the yoyo is dropped with the string fully wound, through what angle does it rotate by the time it reaches the bottom of its fall?
(b) How much arc length has a piece of the yoyo on its outer edge traveled by the time it bottoms out?