$$a_T=\alpha r$$ is the tangential acceleration and where $\alpha$ is the angular acceleration and $r$ is the radius of the circular path.
I know how we get to this mathematically,
If $v=\omega r$ then differentiating this equation we get to the expression that I have above.
But my professor says the angular acceleration comes into picture only when I apply breaks or increase the velocity.
What does this mean?
Best Answer
Angular acceleration $\alpha$ is the rate of change of angular velocity $\omega$ with time. So $\omega$ must increase or decrease somehow if there is an angular acceleration, since $\omega = \frac{v}{r}$ one way it can happen is that $v$ changes.
Presumably your professor was talking about the case where $r$ is constant.