Consider a particle moving in a circle with uniform speed v = |v| and uniform magnitude a = |a| of acceleration. Without introducing any coordinates or basis vectors, do the following.

(a) At any moment of time, let n = v/ν be the unit vector pointing along the velocity, and let s denote distance that the particle travels in its orbit. By drawing a picture, show that dn/ds is a unit vector that points to the center of the particle’s circular orbit, divided by the radius of the orbit.

(b) Show that the vector (not unit vector) pointing from the particle’s location to the center of its orbit is (v/a)²a.