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Math Help - Polar Coordinates - Motion

  1. #1
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    Polar Coordinates - Motion

    A particle P, moving in a plane, has polar coordinates (r , \theta ) referred to the fixed pole O and the initial line in the plane

    Given that the particle moves under a force directed towards towards O, show that at time t r^2 \frac{d \theta}{dt} = h.

    Where h is a constant
    I keep going around in circles with this. a little hint would be nice.

    Many Thanks

    Bobak
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by bobak View Post
    I keep going around in circles with this. a little hint would be nice.

    Many Thanks

    Bobak
    Consider the equations of motion:
    m \frac{d^2x}{dt^2} = a_x
    and
    m \frac{d^2y}{dt^2} = a_y

    What do these equations look like in polar coordinates?
    (Hint: The solution is
    m \left [ \frac{d^2r}{dt^2} - r \left ( \frac{d \theta}{dt} \right )^2 \right ] = f_r
    and
    m \left [ 2\frac{dr}{dt} \frac{d \theta}{dt} + r \frac{d^2 \theta}{dt^2} \right ] = 0
    Make sure you know how to derive these.)

    Or alternately if you are in an advanced enough class, do this using Lagrangian methods. It's easier.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    Consider the equations of motion:
    m \frac{d^2x}{dt^2} = a_x
    and
    m \frac{d^2y}{dt^2} = a_y

    As the force is directed towards the origin that does that mean that a_x \propto -x and similarly for a_y or not ?

    What do these equations look like in polar coordinates?
    (Hint: The solution is
    m \left [ \frac{d^2r}{dt^2} - r \left ( \frac{d \theta}{dt} \right )^2 \right ] = f_r
    and
    m \left [ 2\frac{dr}{dt} \frac{d \theta}{dt} + r \frac{d^2 \theta}{dt^2} \right ] = 0
    Make sure you know how to derive these.)
    This is all new to me, I can't find anything about this in my books, would you mind pointing me to some reading material so I can learn how these results are derived?

    Many Thanks Dan

    Bobak
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