The string in a yo-yo is wound around an axle of radius 0.500 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.200 kg and outer radius 2.00 cm. Starting from rest, it rotates and falls a distance of 1.00 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle.
(a) What is the speed of the yo-yo when it reaches the distance of 1.00 m?
(b) How long does it take to fall? [The translational and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius.]