- #1

- 718

- 9

## Main Question or Discussion Point

I was just reading about torque-free precession and having difficulty seeing how an object's angular velocity vector could at any moment point in a direction that is different than the direction of its angular momentum vector, since that is not possible for an isolated particle

[tex]

\vec \omega = \frac {1}{r^2} ( \vec r \times \vec v)

[/tex]

[tex]

\vec L = m ( \vec r \times \vec v)

[/tex]

(where [tex] r = | \vec r | [/tex])

and in both cases one is just adding up the vector contribution of all the object's constituent particles.

However, the answer to the following question might resolve the matter for me: when an object spins freely in space -- that is, unattached to any other object and with no torque being applied to it -- does the angular velocity vector of each of its particles at any given moment point in the same direction? My intuition says yes, but it is often wrong.

[tex]

\vec \omega = \frac {1}{r^2} ( \vec r \times \vec v)

[/tex]

[tex]

\vec L = m ( \vec r \times \vec v)

[/tex]

(where [tex] r = | \vec r | [/tex])

and in both cases one is just adding up the vector contribution of all the object's constituent particles.

However, the answer to the following question might resolve the matter for me: when an object spins freely in space -- that is, unattached to any other object and with no torque being applied to it -- does the angular velocity vector of each of its particles at any given moment point in the same direction? My intuition says yes, but it is often wrong.