We got that our acceleration vector as a function of time is equal to the negative of our constant angular velocity squared times our position vector

So the magnitude of our position vector, even though the direction is going to change the magnitude of our position vector is not going to change.

So that is its position vector and it is going to change as a function of time as this thing spins around

So everything that I squared off in orange right over here, this is our position vector as a function of time.

Jerk is defined by any of the following equivalent expressions formula_1where formula_2 is acceleration, formula_3 is velocity, formula_4 is position, formula_5 is time.

So now we have position as a function of theta which is actually a function of time.

So the position vector at any time can be written as a sum of its x and y components.

If you take the position vector at any time, the magnitude is r, this angle is theta, its x component, in blue, this vector right over here, the magnitude of the vector, I should say, is going to be r cosine of theta

Now what we want to do is to relate this this is essentially the scalar version of it, so if we wanted to take the magnitudes of both sides, so we're saying the acceleration vector is equal to this constant times the position vector, so let's take the magnitude of both sides of this thing

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