Jerk and Snap in Circular Motion I can understand the physical existence of centripetal acceleration, the orthogonality of that with the linear (tangential) velocity - but how to physically understand jerk and snap in case of uniform circular motion?
 A: For any physical system, a position can in principle be differentiated infinitely many times. 
That's no different in uniform circular motion. The thing that makes it a textbook exercise though is that all components of the position are described by $A\cdot\sin(\omega t+\phi)$ and $A\cdot\cos(\omega t+\phi)$.
This means that the velocity ($d\mathbf{r}/dt$), acceleration ($d^2\mathbf{r}/dt^2$), jerk ($d^3\mathbf{r}/dt^3$) etc. all the way up to infinity, are all described by $\pm\omega^nA\cdot\sin(\omega t + \phi)$ or $\pm\omega^nA\cdot\cos(\omega t + \phi)$. 
The important thing to note though is that there will be minus signs popping up all over the place. The velocity is perpendicular to the position, the acceleration perpendicular to the velocity and in the negative direction of position, the jerk will be perpendicular to the acceleration and in the negative direction of the velocity, and so on.
The takeaway lesson while studying the uniform circular motion is that although the directions are variable, the magnitude of all of them is constant, owing to the identity $\cos^2 + \sin^2 = 1$. Hence the name, uniform circular motion.
It works the same in more dimensions, it just gets more elaborate. This is when the notatational switch to vectors becomes important  -- to be able to focus on the physics, not the mathematical details describing size, orientation, etc.
