Rotational energy convservation probelm, inertia

AI Thread Summary
The discussion revolves around calculating the initial speed required for a small, solid, uniform ball to land 6 cm from a plateau after rolling up a ramp. The key equations involve kinetic energy and conservation of energy, including both translational and rotational components. Participants clarify that the rotational energy can be neglected due to insufficient information about the ball's radius, simplifying the calculations. The problem emphasizes the importance of understanding energy conservation in both kinetic and potential forms. Overall, the focus is on finding the correct initial velocity while navigating the complexities of rotational dynamics.
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A small, solid, uniform ball is to be shot up from point P so it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance (d=6cm) from the right edge of the plateau. The vertical height from P to the top of the plateau is 5 cm, and the game board is s 1.6 cm down from the top of the plateau. A MS paint diagram can be found here: http://imgur.com/rCCPq

Find the speed at witch the ball will be shot at P so it lands 6cm from the plateau.



Relevant equations:
Kinetic energy=.5(Inertia of center of mass)(angular velocity)^2+.5(mass)(velocity)^2
w=angular velocity
I=Inertia of center of mass



So, I've got the basic idea of the problem. I've found the required velocity as the ball leaves the plateau to land in the right spot with projectile motion. Now I'm supposed to use conservation of energy to find the initial velocity.

I don't know exactly how to proceed. The ball starts rotating immediately, so I'd have to include rotational kinetic energy in both in the energy at P, and at the top of the plateau, correct?

So does this look correct? I'm also not sure how to find the inertia used in these equations, so I'd appreciate help with that.

Energy@P= .5(mv^2) +.5(I)(w^2) (only kinetic energy)
Energy@plateu = .5(mv^2)+.5(I)(w^2)+mgy (kinetic energy +potential)
 
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The reason the problem tells you it's a small ball is so you can neglect rotational energy. Even if you wanted to take rotational energy into account, you can't, because no information is provided about the ball's radius.
 
Oh, huh. I guess that makes perfect sense, and makes the problem a lot easier. I wonder why it's in the back of the Rolling, Torque, and Angular Momentum chapter though, if it doesn't include any of those concepts.

Thanks for your help.
 
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