# 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 $$15 kg$$ and radius $$5 m$$, connected by a central spindle of radius $$2 m$$ 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 $$10 N$$ at an angle $$30^\circ$$ 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 $$\dfrac{a\sqrt{b}-c}{d}$$. Where $$a$$ is as large as possible, $$gcd(a,d)=5$$ and $$gcd(c,d)$$=1. What is the value of $$a+b+c+d$$?

• 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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