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## The Question

(Submitted July 21, 1998)

How do celestial bodies (planets, stars, etc.) begin to rotate? Does it happen when matter begins to form into a body?

## The Answer

Most of the rotation of astronomical objects is left over from their formation process. If you are familiar with the conservation of angular momentum you will know that if a slowly rotating object contracts its rotation rate will increase, and this is probably the origin of the rotation of most solar system objects; the cloud of gas and dust which formed the solar system was rotating slowly before it contracted.

Rotational motion is described by the Euler equation, which can be written dL/dt=N, where L is the angular momentum, N is the torque, and d/dt is the time derivative (the instantaneous rate of change). For an object like an asteroid the torque is zero (since there are no external forces acting on it), so the angular momentum is constant. This sounds simple, but the problem lies in the meaning of the angular momentum. For a round object like a ball or a planet the angular momentum is given by the product of the rotation rate or angular velocity (in RPMs or other time units) and the moment of inertia. You should be able to find a definition for the moment of inertia in most introductory Physics textbooks.

I hope this helps,

Tim Kallman
for Ask an Astrophysicist

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