# Stuck on calculating jerk in UCM

## Homework Statement

The question asks to calculate the jerk of an object (both its direction and magnitude) in uniform circular motion.

j=d(a)/dt

## The Attempt at a Solution

I know that the direction is opposite the velocity vector (I did this by drawing a circle and taking a limit of average acceleration as t approaches 0). I also know that the parallel component of jerk is 0 because the parallel component of acceleration in UCM is 0. I am stuck on the magnitude of the perpendicular component. I know that
$$\vec{a}_{\perp} = \frac{v^2}{2}(-r)$$ (the r is a unit vector)... can I just take the derivative of this? wouldn't that be 0? because v^2/r is a constant and there is no t. i am suck.

Last edited:

gneill
Mentor

##r(t) = R (cos(\omega t) \vec{i} + sin(\omega t) \vec{j})##

Should be easy enough to differentiate repeatedly...

##r(t) = R (cos(\omega t) \vec{i} + sin(\omega t) \vec{j})##

Should be easy enough to differentiate repeatedly...
where did you get that parameterized version?

gneill
Mentor
It's just a conversion from polar form to rectangular form of a circle. x = R cos(θ), y = R sin(θ), where θ = ωt to make it time dependent.

It's just a conversion from polar form to rectangular form of a circle. x = R cos(θ), y = R sin(θ), where θ = ωt to make it time dependent.
ok so, j_x = Rw^3sin(wt) and j_y = -Rw^3cos(wt) right?

the problem is however that my prof wanted us to express it interms of v and r. i dont really know how to convert from w to r.... we havent really talked about w yet.

gneill
Mentor
It seems strange that you'd be learning about a concept like jerk without having covered the basics of rotational motion.

##v = \omega r~~ ; ~~a = \alpha r## are the basic relationships between angular and linear velocities and accelerations. You would profit from taking the magnitudes of each of the vectors along the differentiation path: position → velocity → acceleration → jerk. For example, the magnitude of the velocity vector is v = ω R.

It seems strange that you'd be learning about a concept like jerk without having covered the basics of rotational motion.

##v = \omega r~~ ; ~~a = \alpha r## are the basic relationships between angular and linear velocities and accelerations. You would profit from taking the magnitudes of each of the vectors along the differentiation path: position → velocity → acceleration → jerk. For example, the magnitude of the velocity vector is v = ω R.
yeah, it was just one problem out of a list of 10 or so. our teacher kinda talked about w in the last 5 minutes of class on friday, but we haven't touched rotations yet... we havent even begun f=ma (school just started)

Mister T
Gold Member
the problem is however that my prof wanted us to express it interms of v and r. i dont really know how to convert from w to r.... we havent really talked about w yet.

our teacher kinda talked about w in the last 5 minutes of class on friday,

Did your teacher mention that v2/r = rw2?

Most classes have reading assignments in addition to classroom lectures, so maybe it's discussed in more depth there.

Did your teacher mention that v2/r = rw2?

Most classes have reading assignments in addition to classroom lectures, so maybe it's discussed in more depth there.
he wrote on the board that v=ds/dt = r d(theta)/dt ... and d(theta)/dt is the same as w. that is all he talked/wrote about w. so sorry Mister T.... it was hidden in my notes... i guess he did write an equation relating the 2.

Mister T