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A sphere, hoop, and disk race down an incline 30 m in length and at an...

A sphere, hoop, and disk race down an incline 30 m in length and at an angle of 60 degrees. The sphere, hoop, and disk all have the same mass and radius.

a) Using the conservation of energy, derive an equation to calculate the final linear speed as a function of the initial heigh, the acceleration due to gravity, and a constant based on the moment of inertia.

b) Calculate the final linear speeds for all 3 objects.

c) Which object will win the race? Explain using the definition of the moment of inertia.

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