How Are the Velocity & the Centripetal Force Vectors Arranged in Circular Motion?

Hello, my name is Walter Unglaub and this is, "How are the velocity and the centripetal force vectors arranged in circular motion?" So, here I'm going to consider a mass M, denoted by this dot and it's moving in the circular fashion about the center point. So, this could either be an orbit in space, or this mass could be taut, could be tied down to the center via some string or some rope. The point is, this mass will feel a centripetal force vector pointing from the mass to this center or the origin of this trajectory and we denote this centripetal force as F sub c. Now, the velocity vector, specifically the tangential velocity vector is always going to be parallel to the, that point in the orbit. So, in other words, as this mass moves along this circular trajectory, we see that the centripetal force is always pointing from the mass to the center and that the tangential velocity vector is always pointing along that instantaneous tangential path. So, we see that the direction of the velocity vector is always octagonal, or in other words perpendicular to the centripetal force vector. So, you can, we can use this symbol to denote the perpendicular relationship between these two vectors. The tangential velocity is going to be given as the angular frequency times the radius, so the larger the radius the larger the tangential velocity and the centripetal force vector is going to be given as negative mv squared over r, r-hat. So, we see that because of the negative sign, it's an attractive force and it's pulling the mass towards the center. And it has this magnitude and this direction, negative r-hat towards the origin. My name is Walter Unglaub and this is, "How are the velocity and the centripetal force vectors arranged in circular motion?"