# Rotational speeds of the material forming planets should increase, not decrease

We know that planets form as a result of gaseous material revolving around a center of mass that froze to form planets. However shouldn't the angular speed of that matter increase as they go closer to the center to maintain the angular momentum?

Why then the average rotational period of the external planets are faster than that for the terrestrial planets?

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Wait, what? What does your last sentence have to do with the earlier ones? –  Ilmari Karonen Feb 4 '14 at 13:09
Typing error, I just edited - I meant external planets –  Yoda Feb 4 '14 at 20:49

You need to consider which material the planets are formed of.

Terrestrial planets are formed from less material (way less), and with less momentum (since they were orbiting near from the Sun). Gaseous planets (which is another name for external planets, due to their material), also known as gaseous giants, are formed with a lot more of material with a lot more of angular momentum.

Angular momentum formula is $\vec L=\vec r\times m\vec v$.

Orbital speed formula is $\vec v=\vec\omega\times\vec r$.

Thus: $\vec L=\vec r\times m\vec\omega\times\vec r$

Since all vectors are perpendicular:

$L=r^2 m \omega$

Thus a higher mass $m$ makes a higher momentum $L$, and a higher distance to the Sun $r$ makes a quadratically higher momentum $L$.

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What is the relation between less momentum and orbiting near the sun? My question is why terrestrial planets tend to rotate slower than their initial condition, and continue to slow down? –  Yoda Feb 4 '14 at 20:53
@Yoda Answer edited to answer your comment –  Envite Feb 4 '14 at 21:09
Thanks alot for your answer. But I still haven't understood why terrestrial planets slow down with time as they cool and freeze? Could tidal effects from other objects could alone be responsible for that? –  Yoda Feb 4 '14 at 21:17
Who said they slow down with time? –  Envite Feb 4 '14 at 22:51
Isn't our day slowing down with time? –  Yoda Feb 4 '14 at 23:38