Originally Posted by

**Pn0yS0ld13r** Unless im misinterpreting this, this is a relative velocity problem.

Let $\displaystyle \vec{v}_{TE}$ be the velocity of the table relative to Earth. Let $\displaystyle \vec{v}_{PE}$ be the velocity of the particle relative to Earth. And let $\displaystyle \vec{v}_{PT}=\vec{v}_{PE}-\vec{v}_{TE}$ be the velocity of the particle with repsect to the table.

The tangential speed of the table is given by: $\displaystyle \vec{v}_{TE} = r\omega$ where $\displaystyle r$ is the radius of the table.

Since every point on a rotating object has the same angular speed, the tangential speed of the particle at radius L is given by: $\displaystyle \vec{v}_{PE} = L\omega$.

Hence the speed of the particle with repsect to the table is:

$\displaystyle \vec{v}_{PT}=\vec{v}_{PE}-\vec{v}_{TE} = L\omega - r\omega$.