1. ## Wheel

A tire rolls in a straight line without slipping. Its center moves with constant speed $V$. A small pebble lodged in the read of the tire touches the road at $t = 0$. Find the pebble's position, velocity, and acceleration as functions of time.

So $\bold{v} = \dot{r} \bold{\hat{r}} + r \theta \bold{\hat{\theta}}$.

Would it just be $\bold{v} = V \bold{\hat{r}} + Vt \omega \bold{\hat{\theta}}$ and $\bold{a} = -Vt \omega^{2} \bold{\hat{r}} + 2V \omega \bold{\hat{\theta}}$?

Then to find the position as a function of time, integrate the velocity? Actually, should I use Cartesian coordinates instead of polar coordinates?

Thanks

2. Originally Posted by shilz222
A tire rolls in a straight line without slipping. Its center moves with constant speed $V$. A small pebble lodged in the read of the tire touches the road at $t = 0$. Find the pebble's position, velocity, and acceleration as functions of time.

So $\bold{v} = \dot{r} \bold{\hat{r}} + r \theta \bold{\hat{\theta}}$.

Would it just be $\bold{v} = V \bold{\hat{r}} + Vt \omega \bold{\hat{\theta}}$ and $\bold{a} = -Vt \omega^{2} \bold{\hat{r}} + 2V \omega \bold{\hat{\theta}}$?

Then to find the position as a function of time, integrate the velocity? Actually, should I use Cartesian coordinates instead of polar coordinates?

Thanks
I would definitely use Cartesian coordinates here since the center of the wheel is moving linearly and translations look like in polar coordinates. (That and the angular unit vector depends on time, so that complicates the equation. See the other acceleration question you posted.)

-Dan