- #1
tronter
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A tire rolls in a straight line without slipping. Its center moves with constant speed [tex] V [/tex]. A small pebble lodged in the read of the tire touches the road at [tex] t = 0 [/tex]. Find the pebble's position, velocity, and acceleration as functions of time.
So [tex] \bold{v} = \dot{r} \bold{\hat{r}} + r \theta \bold{\hat{\theta}} [/tex].
Would it just be [tex] \bold{v} = V \bold{\hat{r}} + Vt \omega \bold{\hat{\theta}} [/tex] and [tex] \bold{a} = -Vt \omega^{2} \bold{\hat{r}} + 2V \omega \bold{\hat{\theta}} [/tex]?
Then to find the position as a function of time, integrate the velocity?
Thanks
So [tex] \bold{v} = \dot{r} \bold{\hat{r}} + r \theta \bold{\hat{\theta}} [/tex].
Would it just be [tex] \bold{v} = V \bold{\hat{r}} + Vt \omega \bold{\hat{\theta}} [/tex] and [tex] \bold{a} = -Vt \omega^{2} \bold{\hat{r}} + 2V \omega \bold{\hat{\theta}} [/tex]?
Then to find the position as a function of time, integrate the velocity?
Thanks
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