a3 - PHYS2004 (1st Term 10/11) Assignment 3 Section A...

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PHYS2004 (1 st Term 10/11) 1 Assignment 3 Section A (Compulsory – due on 14/10/2010 Thu (before 5:00 pm)) 1. A point P moves on the curve  exp cot ra , in such a way that its radius vector OP  rotates about the origin with the constant angular velocity . Find the radial and transverse components of its velocity, and show that the resultant velocity makes a constant angle with the radius vector. (it is an equiangular spiral ) [50 marks] 2. The velocity of a particle at time t is given by ˆ ˆ ˆ sin 2 2cos2 vt i t j t k  . Find its position as a function of time, given that at time 0 t it was located at the point 3, 1, 3 . Show the velocity and acceleration vectors can never be orthogonal if 3 t . [50 marks] Section B (Optional Questions for STOT groups – please submit in STOT group sessions) 3. A 33 matrix A has elements ij i j ilj l An n n , where i n are the components of a unit vector in 3 . Show that the elements of the matrix 2 A are given by 2 2 ij i j ij
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a3 - PHYS2004 (1st Term 10/11) Assignment 3 Section A...

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