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**1. Homework Statement**

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity v

Diagram: http://i.imgur.com/57qgEHI.png

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity v

_{o}. It travels halfway around the sphere and reaches point B, which is a vertical distance h below A, with a velocity v_{f}. Point A is a radial distance of r_{o}from the vertical centerline and point B is a radial distance of r from the vertical centerline. There is no friction. The goal is to solve for the angle, θ, between the horizontal and the velocity v_{f}.Diagram: http://i.imgur.com/57qgEHI.png

**2. Homework Equations**

Conservation of Momentum, Energy

r

Conservation of Momentum, Energy

r

^{2}+ h^{2}= r_{0}^{2}**3. The Attempt at a Solution**

L

mr

θ=arccos((mr

KE

1/2 mv

v

√(v

θ=arccos((mr

L

_{o}=L_{f}mr

_{o}v_{o}=mrv_{f}cosθθ=arccos((mr

_{o}v_{o})/(mrv_{f}))=arccos((r_{o}v_{o})/(rv_{f}))KE

_{o}+PE_{o}=KE_{f}1/2 mv

_{o}^{2}+mgh=1/2 mv_{f}^{2}v

_{o}^{2}+2gh=v_{f}^{2}√(v

_{o}^{2}+2gh)=v_{f}θ=arccos((mr

_{o}v_{o})/(mrv_{f}))=arccos((mr_{o}v_{o})/(mr√(v_{o}^{2}+2gh)))
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