Unformatted text preview: v is the velocity of the bead. The only real force in this problem is the force of constraint that keeps the bead on the wire. This force does not constrain the radial motion, so we deduce that it has no radial component. In polar coordinates with unit basis vectors e r and e θ , the velocity is v = · r e r + rω e θ , (6) and Eq.(5) yields the explicit result · T = F θ rω. (7) Comparison of Eqs.(4) and (7) gives the following result for the force of constraint F θ = 2 m · rω . (8) This is the general result for this problem ("general" means it applies to all possible cases). If you want a general form that depends only on r (and constants), you have to f nd the f rst integral of Eq.(2), ³ · r ´ 2 = ³ · r ´ 2 + ω 2 ( r 2 − r 2 ) , (9) and use it to eliminate · r from Eq. (8). Then you can see how the constraint force varies with the initial conditions and with r. 1...
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 Fall '10
 Wilemski
 mechanics, Energy, Kinetic Energy, Potential Energy, Goldstein

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