a4 - PHYS2004(1st Term 10/11 Assignment 4 Section...

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PHYS2004 (1 st Term 10/11) 1 Assignment 4 Section A (Compulsory – due on 21/10/2010 Thu (before 5:00 pm)) 1. The curvature of a curve traced out by the position vector   rt is defined as 2 2 3 dr d r dt dt dr dt  . Find , given that (a)  ˆˆ sin cos a t i a t j  , where a is a positive constant. [25 marks] (b) ˆ ˆ sin cos rt t t i t t j . [25 marks] 2. A particle moves along circle: cos rA , under the action of a central force:   Fr . Find   . [50 marks] Section B (Optional Questions for STOT groups – please submit in STOT group sessions) 3. (i) Show that   ij il lj n n ij i j I MM mxx xx  , where 12 il ilk k M mx , m is a true scalar, i x are the components of a polar vector, indices ranging from 1 to 3. (ii) Determine the parity of ij I by considering   ij n n ij i j I .
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PHYS2004 (1 st Term 10/11) 2 4. The polar equation of the orbit of a particle under the action of a central force is given by  1c o s ra  , with 0 a .
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a4 - PHYS2004(1st Term 10/11 Assignment 4 Section...

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