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a11f07 - ( ~ b × ~ c )] i = ± ijk ± klm a j b l c m ....

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PHY 4936 HOME AND CLASS WORK – SET 7 (November 11, 2011) Read Landau-Lifshitz p.96 up to p.101 ( § 31 and § 32). (29) Consider a thin disk composed of two homogeneous halves connected along a diameter of the disk. If one half has density ρ and the other has density 2 ρ , find the expression for the Lagrangian when the disk rolls without slipping along a horizontal surface as shown in the figure (the rotation takes place in the plane of the disk). Due November 18 before class (10 points). y y x x y x θ ( x CM ,y CM ) ¯ y CM 2 ρ ρ (30) A. Calculate ~a × ( ~ b × ~ c ) as superposition of two of its vectors using [ ~a ×
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Unformatted text preview: ( ~ b × ~ c )] i = ± ijk ± klm a j b l c m . Due in class (3 points). B. Does the expression ~a × ~ b × ~ c make sense? Yes or No with reason. Due in class (1 point). (31) The total, conserved energy of a system is given by E = 1 2 MR 2 ˙ θ 2 ± 3 2-8 9 π cos θ ² + MgR ± 1-4 9 π cos θ ² . Consider the following energies: (A . ) E = MgR , (B . ) E = MgR ³ 1-4 9 π √ 2 ! . Are there turning points? If yes, give their θ values. Due November 21 before class (4 points). Read Landau-Lifshitz p.105 up to p.111 ( § 33 and § 35)....
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This note was uploaded on 12/11/2011 for the course PHY 4936 taught by Professor Berg during the Fall '11 term at FSU.

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