What is the angular velocity in the center of a rotating disc?

[Seth Greenberg]

I have a disc. The center of the disc is its center of mass and the motion of the disc is purely rotational (no translation). What is the angular velocity in the center of the rotating disc?

 

[sophiecentaur]

Is this a statement or is there a question in there somewhere?

 

[Seth Greenberg]

What is the angular velocity in the center of the rotating disc?

 

[kuruman]

Assuming that the disk is a rigid body, its angular velocity is $\vec \omega$ at its center and at any other point on it. It is the linear velocity $\vec v=\vec \omega \times \vec r$ that depends on the position vector $\vec r$ and is zero on the axis of rotation. Different points on the disk have different linear velocities but the same angular velocity about the axis of rotation.

 

[Seth Greenberg]

By 'linear velocity' you mean tangential velocity? What happens if $\vec{r}$ is not zero but very, very small, say the plank length $\ell_P$ and $\vec{\omega} = 1$?

 

[kuruman]

By 'linear velocity' you mean tangential velocity? What happens if $\vec{r}$ is not zero but very, very small, say the plank length?

If $\vec \omega$ is constant, as I assume to be the case here, "tangential" and "linear" velocity are the same. When $\vec{r}$ is not zero but very, very small, then the linear velocity classically is not zero but very, very small.

 

[Seth Greenberg]

What is the non-classical case?