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Unformatted text preview: ω of the motion and the radius R of the form: 2 = f( R , G , M S ). ω 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 K-III for this force, again expressing your answer as a relationship between ω and R, (The constant D will necessarily appear in your final expression, but v must not.) ω 2-a = 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? ω = D/m, angular frequency independent of radius....
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This note was uploaded on 01/26/2012 for the course TAM 210 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08