# Sphere mass increase rotation period

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?

• 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 – lurscher Aug 8 '17 at 23:09
• @lurscher Even if the added mass comes straight in with zero angular momentum and sticks? – DJohnM Aug 8 '17 at 23:16
• -1. No effort. What do you think? – sammy gerbil Aug 9 '17 at 12:21

$$L_{total} = L_{initial sphere} + L_{accretion1} + ... + L_{accretion k}$$
$$L = I \omega$$ $$\omega_{final} = \frac{L_{total}}{I_{final sphere}}$$