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Math Help - polar coordinate components and acceleration

  1. #1
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    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

    Last edited by carla1985; February 20th 2013 at 12:02 PM.
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  2. #2
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    Re: polar coordinate components and acceleration

    Hope that makes sense, I had a little trouble with the formatting
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  3. #3
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    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

    then for the radial component
    (-2bhr-2sinθ - 8b2h2r-5cos2θ - 2bh2r-4sinθ)

    which isnt what I want lol
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