How to Solve Angular Kinetics Problem with Inclined Plane and Hoop Release

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    Angular Kinetics
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To solve the problem of a hoop rolling down an inclined plane, it's essential to apply the principles of conservation of energy. The hoop loses potential energy (PE) as it descends, which converts into both translational and rotational kinetic energy. The moment of inertia for the hoop is given by I = MR², and since the hoop rolls without slipping, the final velocity can be determined using the energy conversion. The discussion emphasizes the need to calculate the change in PE and how it translates into kinetic energy to find the time taken to roll down the 16.4 m incline. Understanding these concepts will clarify the approach to solving the problem.
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Homework Statement



A hoop is released from rest at the top of a plane inclined at 16 above horizontal. How long does it take the hoop to roll 16.4 m down the plane?


Homework Equations





The Attempt at a Solution



I know I have to find the final velocity, I know the Inertia is = to

I=MR2

v0=0

Δx=16.4

I also know I need to incorporate some form of constant acceleration or constant angular acceleration to find t.

Im just so confused on how to begin..

Thank you
 
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Consider conservation of energy; The hoop is going downhill, so it's losing height. What's the change in PE? Where does this ΔPE end up? (assume that the hoop rolls and doesn't slip) Can you determine the final velocity from this?
 

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