# polar coordinate components and acceleration

• Feb 20th 2013, 11:54 AM
carla1985
polar coordinate components and acceleration
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 ̇ = 2bhr2 cos θ and hence find r ̈.

(c) Use your answers to (b) to show that the radial component of the acceleration is 8b2h2r5.

So far ive got:
r=2bsin
θ
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

• Feb 20th 2013, 12:03 PM
carla1985
Re: polar coordinate components and acceleration
Hope that makes sense, I had a little trouble with the formatting
• Feb 20th 2013, 03:11 PM
carla1985
Re: polar coordinate components and acceleration
Ok iv worked through to part b) but ive made a mistake somewhere n cant spot it, could someone help me out please:
r.=2bhr-2cos
r..=-2bhr-2sinθ-8b2h2r-5cos2θ