Which Object Reaches the Bottom First? - Solving a Rotational Dynamics Problem

AI Thread Summary
A uniform solid cylinder and a uniform cylindrical shell are released from rest on an incline to analyze their speeds and determine which reaches the bottom first. The conservation of energy equations were applied, revealing that the solid cylinder has a greater velocity than the hollow cylinder. This suggests that the solid cylinder will reach the bottom of the incline first, contrary to the initial assumption that both would arrive simultaneously. The discussion highlights the importance of rotational inertia in determining the dynamics of rolling objects. Ultimately, the solid cylinder's lower moment of inertia allows it to accelerate faster down the slope.
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Homework Statement


A uniform solid cylinder and a uniform cylindrical shell are placed side by side at the top of an incline.If they sre released from rest and roll without slipping,
A)Determine their speeds when they reach the bottom
B)Which objet reaches the bottom first?

Homework Equations


I=mr2 for the cylindrical shell
I=1/2(mr2)
mgyi+1/2(Iw2)+1/2(mv2)=mgyf+1/2(Iw2)+1/2(mv2)



The Attempt at a Solution

I used this conservation of energy equation for each object and got gyi=1/2(r2w2)+1/2(v2) for the hollow cyinder.
then gyi=1/4(r2w2+1/2(v2) for the solid cylinder. since gyi is the same for both i figured that the sollid mass must have a greater velocity and therefore reach the bottom first? Initially i thought they would both have the same velocity and both reach the bottom at the same time. However this result i came up with doesn't quite agree with that.
 
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Thanx, that was perfect:biggrin:
 

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