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    given that  \dot{r} = (6\omega cos\omega t)\mathbf{i} - (4\omega sin\omega t)\mathbf{j} and that  \ddot{r} = (-6\omega^2 sin\omega t)\mathbf{i} - (4\omega^2 cos\omega t)\mathbf{j}

    find at time  t=\frac{\pi}{3\omega} the angle between  \dot{r} and  \ddot{r}

    i'm not really sure 1) what this achieves and 2) how to do it
    any help would be great


    i'm not really sure 1) what this achieves
    Algebra practice most probably in this case. Although physically it finds the angle between the velocity and accelleration vectors of a body, at a specific time.

    2) how to do it
    sub in t for both formulae

    use that

     \dot{r} \bullet \ddot{r} = |\dot{r}| |\ddot{r}| cos \theta

    and rearrange for theta
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Updated: January 27, 2010
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