Analytical Mech Homework Solutions 155

Analytical Mech Homework Solutions 155 - V R 2 mR mR = QR...

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2 V mR mR R φ =− ± ±± 2 R mR mR Q −= ± 2 L mR = ± ± , 2 2 dL mR mRR dt  =+   ± ± ± , LV 2 2 V mR mRR Q φφ += = ± ± L mz z = ± , mz dt z = ± , zz z V mz Q z = G For , using the components of Fm a = G a G from equation 1.12.3: () 2 R RR ± , ( ) 2 FmRR ± ± z , z = From Section 10.2, since R and are distances, and are forces. However, since z R Q z Q is an angle, Q is a torque. Since F is coplanar with and perpendicular to R , QR F = … and all equations agree. (b) 222 22 sin vrr r θ φθ + ± sin 2 m LTV r r r V θφ =−= + + ± L mr r = ± ± , mr dt r = ± , 2 sin mr mr rr ± 2 sin r V mr mr mr Q r −− = = 2 L mr = ± ± , 2 2 mr mrr dt ± ± ± , sin cos mr ± 2 2s i n c o s V mr mrr mr Q θθ +− = = ± ± ± sin L mr = ± ± , 2 2 sin 2 sin 2 sin cos mr mrr mr dt =+ + ± ± ± ± ± , ∂∂ 2 2 sin 2 sin 2 sin cos V mr mrr mr Q + ± ± = is a force . r Q r F Q and Q are torques. Since is in the xy plane, the moment arm for
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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