The Inclined Plane Race: Sphere vs. Hoop

AI Thread Summary
In the inclined plane race between a sphere and a hoop of the same mass, the sphere will reach the bottom first due to its lower moment of inertia compared to the hoop. Both objects start with equal potential energy, but their different moments of inertia result in varying distributions of kinetic and rotational energy as they roll down. The hoop, having a greater moment of inertia, will roll slower than the sphere. Consequently, they will not have equal kinetic energies upon reaching the bottom. The discussion highlights the importance of understanding rotational dynamics in solving such physics problems.
Tricks67
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a sphere and a hoop both of same mass (e.g. 'm') roll down an inclined plane without slipping...which will get to the bottom first..will they have equal kinetic energies when they reach the bottom?
 
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This appears to be homework. If so, you're supposed to show some attempt at solving the problem.
 
nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..
 
Tricks67 said:
nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..

No... though both objects have the same potential Energy at t = 0s, they have different "moments of inertia" and since they are both rolling they have both kinetic and rotational Energy when they reach the bottom of the inclined plane. The hoop will be slower.

Erot = 1/2 J ω²
 
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