1) A yo-yo with an axle diameter of 1.00cm has a 88.0cmlength of string wrapped

Question

1) A yo-yo with an axle diameter of 1.00cm has a 88.0cmlength 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 5.00 cm from the center of the axle.

Part 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?

Part 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

Given:-

Diameter,d=1cm

Radius, r= 0.5 cm

Circumference= 2*pie*r= 3.14 cm

Part A

Number of times the string wrapped= length/circumference= 88cm/3.14 cm= 28 times

1 revolution= 2*3.14 radians

28 revolution= 176 radians

Angle does it rotate by the time it reaches the bottom of its fall = 176 radians

Part B

Arc length has a piece of the yo-yo on its outer edge traveled by the time it bottoms out= 176*5cm= 880cm=8.8m

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