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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

    thanx
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    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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