# Homework Help: Collar On Rod - velocity and acceleration

1. Oct 25, 2008

### nuggets

1. The problem statement, all variables and given/known data
Rod with length PV (P is a pivot point) with collar on rod. Rotation of rod PV about P is $$\theta = 2 t^2$$. distance d of collar from pivot point of rod is $$d = 60t^2 - 20t^3$$. I have to find:
(1) the velocity of the collar
(2) the total acceleration of the collar
(3) the acceleration of the collar relative to the rod

2. Relevant equations

3. The attempt at a solution
Assuming no friction.
I have created the vector r from pivot P to the collar
$$\vec{r} = cos(2t^2)(60t^2 - 20t^3)\hat{i} + sin(2r^2)(60t^2 - 20t^3)\hat{j}$$

I think that the answer to 1 is the first derivative of $$\vec{r}$$
And the answer to 2 is the second derivative of $$\vec{r}$$
And the answer to 3 is the second derivative of d: $$\ddot{d} = 120(1-t)$$

I have calculated $$\dot{\vec{r}}$$ and $$\ddot{\vec{r}}$$, but I have not included them here for brevity.

Am I solving this correctly?

Thank you.