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Motion of a particle in Polar and Normal and Tangential Coordinates watch

    • Thread Starter

    Polar coordinates consist of a scalar radial displacement, r, from a fixed point O, and an angular
    displacement, θ, from some fixed reference angle. The unit vectors for the polar coordinate
    system, er and , move with the particle, so vary in time.

    The normal and tangential coordinate system is particularly useful because, as we have
    observed, the velocity vector is always in the direction of motion (i.e. the tangential direction).
    Therefore we can write the velocity vector in terms of en and et:

    Would someone please expail the bold term. I mean what are they ?
    For example if you to give the position of a particle in a polar coordinate form , how would you give it ... and then what about its velocity and acceleration. Same for the normal and tangential coordinates


    They are unit vectors in the directions the particle would move if you
    (a) increased the radius while keeping theta constant (for {\bf e_r})


    (b) increased theta while keeping the radius constant (for {\bf e_\theta})

    However, this doesn't really answer your question about writing the velocity and acceleration in terms of e_r, e_theta. But to be honest, if you don't know what e_r, e_theta are, to get to understanding how to do velocity/acceleration in those terms would take more time and/or effort than I'm prepared to put in. Here's a document that might help: http://themcclungs.net/physics/downl...oordinates.pdf
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Updated: July 30, 2009
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