Comparison of Rotational Kinetic Energies on an Inclined Plane

AI Thread Summary
The discussion focuses on the comparison of rotational kinetic energies of a solid cylinder and a hollow cylinder rolling down an inclined plane. The solid cylinder, with a lower moment of inertia, will have a greater proportion of its gravitational potential energy converted into translational kinetic energy, resulting in a higher rotational kinetic energy at the bottom. In a frictionless scenario, the hollow cylinder, having a higher moment of inertia, would reach the bottom last due to its greater resistance to rolling motion. The key takeaway is that mass distribution significantly affects the rotational dynamics of the cylinders. Understanding these principles is crucial for analyzing motion on inclined planes.
urapeach
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Here's a question:

A solid cylinder and hollow cylinder of the same mass and radius, both initally at rest, roll down the same inclined plane without slipping.

1) How do their rotational kinetic energies about the center of mass compare at the bottom?

2) If the plane was frictionless, which would reach the bottom first?

Thanks! :-p
 
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Consider the mass distribution. If both cylinder have the same mass and radius, which one will have the larger value of I?
 
Also remember in rotational problems such as this the total energy is that of the kinetic and rotational energy summed. Just thought that might help in the second part of the question.
 

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