Problems and solutions I

T t this gives the analog of the momentum form of the

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Unformatted text preview: entiation. Using this we can differentiate the angular momentum for a particle. This gives: „ „t L= „” ”„ ” ”” r ä p + rä p = v ä m v + r ä F net = 0 + tnet . „t „t This gives the analog of the momentum form of the second law F net = „ p ê „ t. This is tnet = „ „t L. 4 | Chapter I - Rotational Dynamics and Equilibrium A System of Particles F 12 m1 ext F1 F 13 ” r 13 ” r1 ” F 31 ” r3 r 12 ” r2 ext F3 ” r 23 F 23 m2 m3 F 32 ext F 21 F2 Interactive Figure ”” ” In the preceding chapter we considered a three particle system with masses m1 , m2 and m3 at positions r1 , r2 and r3 . As before, we write the ext ” forces on m1 as a sum of internal forces F 12 and F 13 and external forces F 1 . The cross products of this with r1 gives the net torque. The torques for m2 and m3 break up similarly. „ ext ” ” ” tnet,1 = r1 ä F 1 + r1 ä F 12 + r1 ä F 13 = L1 „t „ ext ” ” ” tnet,2 = r2 ä F 2 + r2 ä F 21 + r2 ä F 23 = L2 „t „ ext ” ” ” tnet,3 = r3 ä F 3 + r3 ä F 31 + r3 ä F 32 = L3 „t To concentrate on the bulk motion of our system we sum over these expressions. In the previous case with forces the internal forces canceled due to Newton's third law. Here we need to make an additional assumption that the force...
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This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.

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