A yo-yo with an axle diameter of 1.00 cm has a 90.0 cm length of string wrapped

Question

A yo-yo with an axle diameter of 1.00 cm has a 90.0 cm length of string wrapped around it many times in such a way that the string completely covers the surface of the axle, but there are no double layers of string. The outermost portion of the yo-yo is 5.00 cm from the center of the axle. a) If the yo-yo 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 yo-yo on its outer edge traveled by the time it bottoms out?

Explanation / Answer

radius of axle, r = d/2

= 1/2

= 0.5 cm

= 0.005 m

a) apply, s = r*theta

==> theta = s/r

= 0.9/0.005

= 180 rad

b)here angular dispalcement of axle and Yo-Yo outer part is same.

Apply, arc length of yo-yo outer part, S = R*theta

= 0.05*180

= 9 m

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