Setting O as the origin of the coordinate system and \vec{e}_r in the direction of O to O', would the following components be correct?
r_O' = \frac{r}{3} \vec{e}_r
r_{O'm} = -r cos(\theta + \omega t) \vec{e}_r
r_{OM} = r_O' + r_{O'm}
Homework Statement
A horizontal turntable rotates at a constant rate ω about a fixed vertical axis through its center O. A particle of mass m can slide in a fictionless circular groove of radius r centered at O' which is r/3 from O. What is the radial acceleration of m in direction O'm...