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Minimum period of rotation and gravity

  1. Jan 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider a planet with uniform mass density p. If the planet rotates too fast, it will fly apart. Show that the minimum period of rotation is given by:

    T = (3 pi)^(1/2)
    ......(G p)^(1/2)

    What is the minimum T if p = 5.5 g/cm^3?

    2. Relevant equations

    T = 2 pi r

    v = (G m)^(1/2)

    3. The attempt at a solution

    I combined the two equations to have:

    T = 2 pi (r)^(3/2)
    .......(G m)^(1/2)

    I found dr/dT to have:

    3 pi (r)^(1/2)
    (G m)^(1/2)

    What am I doing incorrectly?
  2. jcsd
  3. Jan 10, 2007 #2
    How does dr/dT relate to this problem???

    Read the question carefully, and try to use the "givens." In this case, you are required to find the minimum of period of rotation, which is given as a function of the velcocity.

    Your substitution was right. Note that the planet's density is also provided. Remember that density = mass.volume
  4. Jan 10, 2007 #3
    Hmmm, so am I not supposed to find a derivative somewhere, or?
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