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Centrifugal acceleration in rotating frame

  1. Feb 3, 2016 #1
    1. The problem statement, all variables and given/known data
    I have a doubt about the way to calculate the centrifugal acceleration for a point P that rotates with angular velocity ##w_1## wtr a inertial frame on a platform that rotates with angular velocity ##w## (##w_1>w)##. I want to find the centrifugal acceleration in the rotating frame.

    2. Relevant equations
    Centripetal force = - centrifugal force

    3. The attempt at a solution
    I don't have clear if I have to consider the relative angular velocity ##w_r=w_1-w##
    and write ##a'_{centrifugal}=w_r^2 r##

    or ##a_{centrifugal}=w_1^2 r- w^2 r##
     
  2. jcsd
  3. Feb 3, 2016 #2

    andrewkirk

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    How is this question different from the one you asked in this thread, and which was answered in that thread?
     
  4. Feb 3, 2016 #3
    you are right, it's similar. But it is a more general question and I wasn't sure that I wouldn't be wrong applying the reasoning that you linked...
    Now I can conclude that ##a_{centrifugal}=w_r^2 r## and I don't have to subtract ##w_1^2r## and ##w^2r##... but what do I obtain if I do ##w_1^2r -w^2r##? A lot of thanks


    ____

    edit: Mmmmh, no. This question is different from the question that I have posted some days ago.
    In that question I asked the acceleration of the ball in a non inertial frame.
    In this question, I'm asking for the centrifugal acceleration that the point P "feels" in the frame of the platform.
    In the question you linked, I asked for a', the total acceleration that the point P "feels" in the platform frame.
     
    Last edited: Feb 3, 2016
  5. Feb 3, 2016 #4

    andrewkirk

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    'Felt' acceleration is frame independent. If it weren't, whether a dropped class breaks upon hitting the floor would depend on what frame of reference we were using to measure it. So 'in the frame of the platform' is meaningless.
    Also, note that centrifugal acceleration of a rotating body with constant distance from the axis of rotation will always be negative, because it has to undergo a positive centripetal acceleration in order to maintain the constant distance.
    In general, the word 'centrifugal' is best used only for things like string tensions and felt accelerations. 'Centripetal' acceleration is the important concept, which is what keeps the body in circular motion.
     
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