Find the pebble's position, velocity, and acceleration

  • Thread starter tronter
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  • #1
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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
 
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Answers and Replies

  • #2
Avodyne
Science Advisor
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You need to do this in cartesian coords, because the center keeps moving.
 
  • #3
186
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So use the transformations [tex] x = r \cos \theta [/tex], [tex] y = r \sin \theta [/tex]?
 
  • #4
I had to do a problem similar to this, and I still don't understand it....
 

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