I'm stuck on the second part of this question:
Suppose that a particle moves in a plane with trajectory given by thepolar equation r = 2b sinθ for some constant b > 0.
(i) Show that this can be written in Cartesian coordinates as,x2 + (y − b)2 = b2,
This is the equation for a circle of centre (0, b) and radius b.
[Hint:recall that r2=x2+y2 and y=rsinθ]
(ii) Suppose that the transverse component of the acceleration is zero.
(a) Prove that r2θ ̇ = h is constant.
(b) Assuming that r =/ 0, show that r ̇ = 2bhr−2 cos θ and hence find r ̈.
(c) Use your answers to (b) to show that the radial component of the acceleration is −8b2h2r−5.
So far ive got:
r ̇=2bcosθθ ̇
so the transverse co-ordinate is (4bcosθθ ̇^2+2bsinθθ ̈) the dots indicating 1st and second derivative, usually above the r's and theta's