We found in lecture that for a particle traveling in a circle the acceleration c

Question

We found in lecture that for a particle traveling in a circle the acceleration can be broken into a part parallel to the velocity and a part perpendicular to it: a_circle =a| + a,where{a|=dv/dtv a =v^2/r(-r) Assuming an object is traveling around the circle at a constant speed, calculate the magnitude (in terms of v and r) and describe the direction (in terms of the direction of motion of the object and/or the position vector pointing to it from the center of the circle) of the jerk vector on the object, where jerk is defined by: j=da/dt

Explanation / Answer

let a thing should motion with variable speed on a circular path of radius r

on time t it reach point p and at (t +delta t) it reach point p, where it velocity is (V+ delta V)

the accleration on tangent direction

   at = V, cosQ - V / delta t

cosQ = 1

   at = V, - V / delta t

here V, = V + delta V

so at = delta V / delta t

if t is minimum so

   at = dV / dt Ans

accleration on radious side

ar = V, sinQ / delta t

sinQ = Q

so ar = V, Q / delta t

here V, = V + delta V

so = V Q + delta V Q / delta t

on neglating delta V Q

ar = V Q / delta t

   = V W where W = V / R

ar = V2 / R Ans

2.

The method shown above works even when acceleration isn't constant. Let's apply it to a situation with an unusual name — constant jerk. (No lie, that's what it's called.) Jerk is the rate of change of acceleration with time.

This makes jerk the first derivative of acceleration, the second derivative of velocity, and the third derivative of displacement.

The SI unit of jerk is the meter per second cubed.

An alternate unit is the g per second.

Jerk is not just some wise ass physicists response to the question, "Oh yeah, so what do you call the  third derivative of displacement?" Jerk is a meaningful quantity

j = da dt

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