Final answer:
The percentage of kinetic energy of a rolling sphere that is purely rotational can be determined using the given formula for the moment of inertia of a sphere and the formula for rotational kinetic energy.
Step-by-step explanation:
The percentage of kinetic energy of a rolling sphere that is purely rotational can be determined using the given formula for the moment of inertia of a sphere, I = 2/5 MR². The rotational kinetic energy (Krot) of a sphere can be calculated using the formula Krot = 1/2 Iω², where ω is the angular velocity.
Since the sphere is rolling, its linear velocity (v) and angular velocity (ω) are related by the equation v = Rω, where R is the radius of the sphere. Substituting this relation into the formula for rotational kinetic energy, we get Krot = 1/2 (2/5 MR²) (v/R)².
The total kinetic energy (Ktotal) of the sphere can be calculated using the formula Ktotal = 1/2 Mv². Dividing the rotational kinetic energy by the total kinetic energy and multiplying by 100 will give us the percentage of kinetic energy that is purely rotational: (Krot/Ktotal) * 100 = [(1/2) (2/5 MR²) (v/R)²] / [(1/2) Mv²] * 100.