Physics

A bicycle has wheels of radius 0.32 m. Each wheel has a roatational inertia of 0.080 kg•m^2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels?

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  1. The rotational kinetic energy of one wheel is

    1/2 * I * w^2

    where I is the moment of inertia of the wheel, w is the angular speed of the wheel.

    The total kinetic energy of the system is the sum of the rotational kinetic energies of each wheel, plus the translational kinetic energy of the bicycle:

    K = 1/2*I*w^2 + 1/2*I*w^2 + 1/2 *m*v^2

    v = w^2*r^2
    where v is the translational speed of the bicycle, and r is the radius of the bicycle's tire

    K = I*w^2 + 1/2*m*w^2*r^2

    the fraction is (I*w^2) / (1/2*m*w^2*r^2)

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