Is there jerk on Uniform Circular Motion? I was reading my textbook and I encountered a section where it explains that Centripetal Acceleration is not constant, thus, I wonder if jerk exists in Uniform Circular Motion? The textbook states that it happens due to the continuous change on the vector's direction. So, pretty much. Does jerk manifest? or, if it does not, why?
 A: As other answers and comments said, yes there is jerk. But it doesn't mean what you think. In everyday use, a jerk is a sudden acceleration, like a sudden yank on a rope. That is not what centripetal acceleration is like.
If you tie a rope to a rock and swing it around your head, you must pull on the rope to keep it moving in a circle. That is centripetal force and centripetal acceleration. If the rock is circling at a constant radius and speed, the magnitude of the force does not change. The direction smoothly changes. You have to keep pulling toward yourself as the rock moves around you.
The other answers about jerk, snap, crackle, and pop are apparently technical terms for higher derivatives of velocity. Though I had never heard of them before this question. They are not in common use. And these technical definitions do not imply sudden accelerations either.
Jerk is the derivative of acceleration. It is a semi-good name. It makes more sense to apply it to the derivative of force than acceleration.
Suppose you are pulling with constant force on a rope, trying to move a stuck object. You give the rope a yank. The force momentarily rises and then returns to its former value. The derivative of force reasonably fits the idea of jerking the rope, even if the object is still stuck. If the object breaks free and there is a non-zero acceleration, then the derivative of acceleration also reasonably fits the idea.
Jerk is a non-zero vector in uniform circular motion. But the motion does not fit the everyday idea of jerking the rope.
A: Jerk is the change in acceleration.  If acceleration is changing, then there is jerk.  Since there is a changing acceleration in circular motion, there is jerk in circular motion.
I'm not entirely sure what you mean by "manifest" though.  It's simply something that can be measured.
A: Others have explained it well, but I wanted to add another point.
When I think of "jerk", I think of amusement park rides that "jerk" my head around.  With constant acceleration (zero jerk), it's easy to keep your head steady with a constant application of your neck muscles.  When acceleration changes quickly (non-zero jerk), it's hard to keep your head from moving relative to your body.
When I first read your question I thought "It's easy to keep your head steady on a carnival ride shown below, so there must be zero jerk".  In this case, I think your body has zero jerk in the rotating reference frame centered at the ride's axis.  In other words, since your body is rotating along with the reference frame, you don't feel the jerk.

