I'm having an issue, which is that my equation for acceleration in constant speed circular motion is different from the prof's. We are essentially told to derive an equation based on a particle travelling at v metres per second. I reasoned that in half a period, the particle reverses velocity, therefore acceleration is 2v/(T/2). Then for T I used (2*pi*r)/v, such that T/2 = (pi*r)/v. Consequently this gives me an equation for angular acceleration of A = (2v^2)/(pi*r)
However, the prof's equation states that A = v^2/r
Am I doing something wrong?