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Collar On Rod - velocity and acceleration

  1. Oct 25, 2008 #1
    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 [tex]\theta = 2 t^2[/tex]. distance d of collar from pivot point of rod is [tex]d = 60t^2 - 20t^3[/tex]. 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
    [tex]\vec{r} = cos(2t^2)(60t^2 - 20t^3)\hat{i} + sin(2r^2)(60t^2 - 20t^3)\hat{j}[/tex]

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

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

    Am I solving this correctly?

    Thank you.
     
  2. jcsd
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