That's one huge yo-yo!

In an alien planet, an alien wants to play yo-yo. The gigantic yo-yo consists of two solid disks, each of mass 15kg15 kg and radius 5m5 m, connected by a central spindle of radius 2m2 m and negligible mass. A string is coiled around the central spindle. The yo-yo then is placed upright on a rough flat surface and the string is pulled gently with a tension of 10N10 N at an angle 3030^\circ to the horizontal. The pull is gentle enough to ensure that that yo-yo does not slip nor lifts off the ground.

The acceleration of the center of mass of the yo-yo can be expressed in the form abcd\dfrac{a\sqrt{b}-c}{d}. Where aa is as large as possible, gcd(a,d)=5gcd(a,d)=5 and gcd(c,d)gcd(c,d)=1. What is the value of a+b+c+da+b+c+d?

  • Assume that the only difference between the planet and earth is the size of the inhabitants and the planets, nothing else.
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