Final answer:
To calculate the fraction of the kinetic energy that is rotational for the bicycle wheels, we determine both rotational and translational kinetic energies using the formulas for their respective kinetic energies and the moment of inertia, mass, and radius provided, and then divide the rotational kinetic energy by the total kinetic energy.
Step-by-step explanation:
To calculate the fraction of the total kinetic energy of a bicycle that is the rotational kinetic energy of the wheels, we need to determine both the translational and the rotational kinetic energies. The total mass of the bicycle including the wheels and the rider is given as 650 kg, and each wheel has a rotational inertia (moment of inertia) of 0.0800 kg·m2 about its axle. Given that the bicycle is coasting at constant speed, the rotational kinetic energy (KErotational) for each wheel can be represented by the formula KErotational = 1/2 I ω2, where I is the moment of inertia and ω is the angular velocity.
We do not have the angular velocity directly, but we can find it knowing that the translational speed (v) of the bicycle is the same as the linear velocity at the rim of the wheels, which can be related through the equation v = ωr, where r is the radius of the wheel. Hence, for both wheels together, the rotational kinetic energy is KErotational = 1/2 (2 × I) ω2. Note that we multiply by 2 to account for both wheels.
The translational kinetic energy (KEtranslational) for the rest of the bicycle and the rider is given by KEtranslational = 1/2 mv2, where m is the mass excluding the wheels. Assuming negligible mass for the wheels compared to the total mass, m will be close to the total mass of the bike and rider.
Finally, we can calculate the fraction of rotational kinetic energy by dividing the rotational kinetic energy of the wheels by the sum of both rotational and translational kinetic energies: fraction = KErotational / (KErotational + KEtranslational).