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Physics Circular motion formulae derivations!!!

  • 14-06-2008 11:24PM
    #1
    mike-gunners
    Closed Accounts Posts: 33 ✭


    derivations in circular motion:

    1.v = rw

    s = r 8

    s/t = r8/t (dividing both sides by "t").

    but s/t = v and 8/t = w

    :- v = rw (subsituting for V and W ).

    2. T^2 = 4(pi)^2r^3/GM

    when a satellite is orbiting a planet eg earth, there is a force of attraction between them and since this is the only force on the satellite, therefore this is the resultant force and is the centripetal force.

    so F = GMm/R^2 = mRw^2 (R=Radius , M=mass of earth, m-mass of satellite, G=universal gravitation constant, w=angular velocity).

    => w^2 = GM/R^3

    The Periodic time is T=2(pi)/w
    => T^2 = 4(pi)^2/w^2.

    => T^2 = 4(pi)^2/GM/R^3 (subsituting for w^2).

    => T^2 = 4(pi)^2r^3/GM.


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