Hoop and Cylinder Motion

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

Experimenters: Walter Shields and Karen Tolmich

Conservation of energy gives:

For rolling without slipping, ω = v/r. The difference between the hoop and the cylinder comes from their different rotational inertia.

Solving for the velocity shows the cylinder to be the clear winner.

The cylinder will reach the bottom of the incline with a speed that is 15% higher than the top speed of the hoop. The hoop uses up more of its energy budget in rotational kinetic energy because all of its mass is at the outer edge.

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Rotation concepts

Rotational kinetic energy concepts
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