I am trying to calculate the "relative linear velocity" of a particle moving over a rotating object.
According to this paper (section 2.2) I am reading the relative linear velocity is calculated by:
$$ v'= v - \omega r $$
Where $v$ is the velocity of the particle, $\omega$ the angular velocity of the rotating object and $r$ the radius of the object.
What I don't understand is why subtract? For high angular velocities with low particle velocities that will produce a negative velocity. The particle's surely not traveling backwards relatively, if the particle is traveling in the same direction as the rotation?