Hoop and Cylinder Motion

Given a race between a thin hoop and a uniform cylinder down an incline. Which will win?

Do the relative masses of the hoop and cylinder affect the outcome? Do the relative radii of the hoop and cylinder affect the outcome? Both start at the same height and have gravitational potential energy = mgh. Assume that they roll without slipping.

Hoop and Cylinder Motion

Given a race between a thin hoop and a uniform cylinder down an incline. Which will win?

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Hoop and Cylinder Motion

The cylinder wins the downhill race because it doesn't use up as much of its energy resource in rotational kinetic energy. All of the hoop's mass is at the maximum radius, contributing more to its moment of inertia. Since the angular velocity is proportional to the linear velocity, it has to put more of its energy into rotational kinetic energy. Load movie