# 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?

• 'but how to physically understand jerk and snap in case of uniform circular motion?' That's an oxymoron. In uniform circular motion, centripetal acceleration is constant. – Gert Jan 9 '17 at 14:18
• @Gert constant in magnitude, not direction. – Rody Oldenhuis Jan 9 '17 at 14:26
• When you say "physically understand," are you talking about an intuitive concept, or is just taking the derivatives of position, velocity, acceleration, jerk, snap... etc the kind of answer you are looking for? – Cort Ammon Jan 9 '17 at 14:42
• I can "feel" centripetal force in uniform circular motion. What about Jerk ? I mean, jerk is change in acceleration with time. How and what can we 'feel' about that ? – novice Jan 9 '17 at 15:07
• @novice What coordinate frame are you in when you "feel" the centripetal force? If you are in a frame that is rotating with the object, you need to allow for your own rotation. If you were moving in a circle but always facing in the same direction, you would "feel" that the centripetal acceleration was changing direction as you moved round the circle. – alephzero Jan 9 '17 at 16:47

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 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.