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Homework Help: Angular momentum of the sun and a white dwarf

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data

    The Sun rotates about its own axis once every 26.0 days. Its mass is m_sun = 2.0E30 kg and radius is r_sun = 7.0E8 m. Assume that the Sun is a solid sphere with uniform density.

    Astrophysicists predict that the Sun will collapse into a white dwarf in some billions of years. Its density will be high, and its radius 5.8E6 m. Assume the mass of the Sun to be unaltered (a good approximation for our calculation).

    (i) What is the Sun's angular momentum now?
    (ii) What is the Sun's angular momentum as a white dwarf?
    (iii) How long will it take for the white dwarf Sun to rotate about its own axis?

    2. Relevant equations

    I = (2/5)*m*r^2
    L = Iω = Iωk (k being the z-axis unit vector)

    3. The attempt at a solution

    ω_sun = (2pi)/(26 days) = 2.8E-6 rad/s

    L = I_sun*ω_sun*k = (2/5)*m_sun*r_sun²*ω_sun*k = (2/5)*2.0E30 kg * (7.0E8 m)² * ω_sun * k = 1.1E42 kgm²/s

    I don't know the new spin angular velocity of the white dwarf, do I? If I leave ω_white = ω_sun the formula for L above with inserted new value for radius r_white gives appr. 7.5E37 kgm²/s k, ie. the angular momentum is lowered. Can this be correct?

    I don't know what to do here. I want to find the new period T, but I suspect there is something odd in (ii). Is there a relation I have overseen?

    Thanks for any help.
  2. jcsd
  3. Feb 15, 2009 #2

    Doc Al

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    Staff: Mentor

    I didn't check the arithmetic, but the method is correct.

    What's required to change the angular momentum? Does that apply here?
  4. Feb 15, 2009 #3
    Ah, so you are saying to me: Angular momentum is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.

    Then I set up T_white = ( I_white * 2pi * k ) / L which gives a rotation period of 1.5E2 s or 150 s.

    (Mathematically: L features numbers and the unit vector k; In the calculation above I mentally ignored the unit vector because it was a feature of both nominator and denominator -- I'm I right to do this?)
  5. Feb 15, 2009 #4

    Doc Al

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    Staff: Mentor

    All good.
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