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Unformatted text preview: of the motion and the radius R of the form: 2 = f( R , G , M S ). 2 = G M S / R 3 R v m M s page 2 (c) Consider uniform circular motion of a body of mass m about a central force which depends on velocity: F = Dv a R b where D is a constant and a and b are known exponents. Derive KIII for this force, again expressing your answer as a relationship between and R, (The constant D will necessarily appear in your final expression, but v must not.) 2a = D R a + b 1 /m (d) For the case a = 0 and b = 2, verify that your answer to part(c) collapses to that for part (b) (this is an excellent limiting behavior check). (e) Evaluate your answer to part (c) for the case a = 1 and b = 0. How does the angular frequency depend on radius for a force of this nature? = D/m, angular frequency independent of radius....
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 Fall '08
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