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What is the effect on period of rotation of a sphere as mass and volume increase, when increasing mass makes no contribution to angular momentum?

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  • $\begingroup$ angular momentum is proportional to mass, length to axis and velocity integrated over the mass region. An increase of mass will always make a contribution to angular momentum, unless the shape changes as mass is increased $\endgroup$ – lurscher Aug 8 '17 at 23:09
  • $\begingroup$ @lurscher Even if the added mass comes straight in with zero angular momentum and sticks? $\endgroup$ – DJohnM Aug 8 '17 at 23:16
  • $\begingroup$ -1. No effort. What do you think? $\endgroup$ – sammy gerbil Aug 9 '17 at 12:21
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Angular momentum (like linear momentum) is a constant for a system with no external forces/torques.

Calculate the angular momentum of the starting material (in this case it should include the initial rotating sphere and all the accreting material).

$$ L_{total} = L_{initial sphere} + L_{accretion1} + ... + L_{accretion k}$$

Then use the moment of inertia of the now larger sphere and the known angular momentum to calculate the rotational velocity.

$$ L = I \omega $$ $$ \omega_{final} = \frac{L_{total}}{I_{final sphere}}$$

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  • $\begingroup$ Mass theoretical increase is at a non defined point within volume of the sphere in the form of mass = E/c*c. $\endgroup$ – user165899 Aug 9 '17 at 23:39
  • $\begingroup$ Known variables, P2, Period of rotation at a known time in the past T2. P1, period of rotation in the present, T1. Mass and volume are known in the present. Is it possible to calculate mass and volume at T2? $\endgroup$ – user165899 Aug 9 '17 at 23:50

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