Dynamics, polar coordinate system

  1. i have been set the following question

    theta = 3r^2
    find the magnitude of the acceleration when

    r=0.8 m
    dr/dt = 4ms^-1
    d^2r/dt^2 = 12 ms^-2

    my working followed the process of calculating angular velocity with these conditions and angular acceleration with these conditions then plugging them into the acceleration formula for a polar coordinate system.

    when doing this i get

    a(radial) = -282.912 ms^-2 (componant along the radius)
    a(theta) = 218.88 ms^-2 (componant perpendicular to radius)

    using pythagoras to calculate the magnitude of the resultant acceleration i get a value 357.7 ms^-2

    a value my dynamics lecturer is prompt to tell me is WRONG. perhaps someone can help me...PLEASE
  2. jcsd
  3. Meir Achuz

    Meir Achuz 2,073
    Science Advisor
    Homework Helper
    Gold Member

    Your numbers are wrong. I don't see how you could get them.
    The radial acceleration is GIVEN to you as 12 m/s^2.
    You have to relate d^2theta/dt^2 to d2r/dt^2 by differentiating the equation
    theta=3r^2 twice. Then rd^2theta/dt^2 s gives a(theta).
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