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Object whose gravity makes milk behave as in spinning bowl

  1. Jun 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Let us explore whether there is any way to distinguish acceleration due to rotation from acceleration due to a gravitational force. Imagine a deep bowl with a small volume of milk in it.
    (a) What happens to the milk when you spin the bowl about a perpendicular axis that runs through the center of the bowl bottom? (b) What is the shape of an object that exerts a gravitational force that could make the milk behave in a similar fashion?


    2. Relevant equations
    This question is a rotational version of the accelerating elevator. The person in the elevator cannot tell if the elevator is accelerating of if there is a large mass below the elevator producing a gravitational field. My take on this question is that we need to find the mass that would make the observer in the bowl see the milk rise up the sides, just as he does when the bowl spins. Thus, he could not tell if the milk was rising up due to spinning of the bowl or due to the mass outside that creates the same effect by gravity.


    3. The attempt at a solution
    Part (a) is easy, but I cant' get a grip on part (b). An observer inside the bowl and spinning with it would think there was a force pulling the milk up and away from the center, like a tide rising. Would a giant doughnut positioned above the bowl produce the gravitational field to do that?
     
  2. jcsd
  3. Jun 21, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    I would expect that you can get some curved surface with a doughnut-shaped mass, but I am not sure.
     
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