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Math Help - Centripetal Force

  1. #1
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    Angry Centripetal Force

    A body of mass 9 kg moves in a (counterclockwise) circular path of radius 5 meters, making one revolution every 9 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component.

    Compute the centripetal force acting on the body. (As a vector of 2 components.)

    I know the first part of the two components, but I need help solving for the last parts.

    <[(-9(10\pi/9)^2) / 5][cos((10\pi/9)t) / ... ], [(-9(10\pi/9)^2) / 5][sin((10\pi/9)t) / ... ]>

    Please help!
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  2. #2
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    uniform circular motion with angular speed \omega = \frac{2\pi}{9} \, rad/sec

    position ...

    x = 5\cos(\omega t)

    y = 5\sin(\omega t)

    velocity ...

    \frac{dx}{dt} = -5\omega\sin(\omega t)

    \frac{dy}{dt} = 5\omega\cos(\omega t)

    acceleration ...

    \frac{d^2x}{dt^2} = -5\omega^2\cos(\omega t)

    \frac{d^2y}{dt^2} = -5\omega^2\sin(\omega t)
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  3. #3
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    Quote Originally Posted by skeeter View Post
    uniform circular motion with angular speed \omega = \frac{2\pi}{9} \, rad/sec

    position ...

    x = 5\cos(\omega t)

    y = 5\sin(\omega t)

    velocity ...

    \frac{dx}{dt} = -5\omega\sin(\omega t)

    \frac{dy}{dt} = 5\omega\cos(\omega t)

    acceleration ...

    \frac{d^2x}{dt^2} = -5\omega^2\cos(\omega t)

    \frac{d^2y}{dt^2} = -5\omega^2\sin(\omega t)
    Thank you so much!! I'm so rusty with physics, I didn't know how to use the information given.
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