A yo-yo with an axle diameter of 2.00cm has a 80.0cm 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 yo-yo is 4.00 {\rm cm} from the center of the axle.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?

1 answer

The circumference of the axel is
L=πd,
the string wraps around the axel
N=s/L= s/ πd.
The angle of rotation is
φ=2πN=2 πs/ πd=2s/d= =2•80/2=80 rad