Results 1 to 2 of 2

Math Help - Wheel

  1. #1
    Member
    Joined
    Aug 2007
    Posts
    239

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Quote Originally Posted by shilz222 View Post
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cog and wheel
    Posted in the Geometry Forum
    Replies: 12
    Last Post: April 19th 2011, 08:16 AM
  2. ferris wheel..
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: April 2nd 2011, 10:23 AM
  3. Ferris Wheel WS
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: January 20th 2011, 05:50 PM
  4. Replies: 2
    Last Post: November 18th 2010, 09:03 AM
  5. bicycle wheel
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 20th 2010, 05:24 AM

Search Tags


/mathhelpforum @mathhelpforum