Unformatted text preview: (5 pts) c. Find the translational and rotational energy of the ball. (5 pts) 3. (20 pts) Vector calculus a. Find the gravitational potential ) ( r Φ and gravitational field ) ( r g inside and outside of a solid sphere with uniform density ρ . (6 pts) b. In Cartesian coordinates, explicitly show that = × ∇ g . (7 pts) c. In Cartesian coordinates, explicitly demonstrate that the Poisson equation holds. (7 pts) 4. (20 pts) A ball slips down a smooth parabolic hill (described by the function 2 x y − = ) under gravity, as shown. a. Find the velocity v of the ball at a given location x . (8 pts) b. Find the force f exerted on the ball by the slope at a given location x . (12 pts) g l ) , ( g h...
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 Spring '09
 R
 Mass, General Relativity

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