Hoop and Cylinder MotionGiven a race between a thin hoop and a uniform cylinder down an incline. Which will win?
The analysis uses angular velocity and rotational kinetic energy. For rolling without slipping, the linear velocity and angular velocity are strictly proportional. 
Index Rotation concepts Rotational kinetic energy concepts  

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Hoop and Cylinder MotionGiven a race between a thin hoop and a uniform cylinder down an incline. Which will win?
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. Show more detailLoad movie 
Index Rotation concepts Rotational kinetic energy concepts  

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Hoop and Cylinder MotionGiven a race between a thin hoop and a uniform cylinder down an incline, rolling without slipping. Which will win? Mass and radius cancel out in the calculation, showing the final velocities to be independent of these two quantities.

Index Rotational kinetic energy concepts  

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