how to find tangential acceleration

Question

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How can I find the tangential and normal components of the acceleration vector at t=2 for: r(t)= ti + (t^2-1)/2j + (t^2+1)/2k

I found the velocity vector at t=2 to be <1,2,2> and acceleration vector to be <1,0,1>

What goes next for the tangential and normal components of acceleration vector?

asked Sep 16 '15 at 15:35

user3015986user3015986

523 3 gold badges 10 silver badges 24 bronze badges

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5

$\begingroup$ Is that all the information you have ? What have you tried ? $\endgroup$

Sep 16 '15 at 15:38
$\begingroup$ so tangential acceleration seems like = V dot A / magnitude of V, so I dot product the acceleration and velocity the divide by magnitude of V which is 3. Am I right? The answer seems to be 1 for tangential acceleration $\endgroup$

Sep 16 '15 at 15:45
$\begingroup$ You are almost there. See answer posted by Onomnomnom $\endgroup$

Sep 16 '15 at 15:47
$\begingroup$ I fixed my question. Somehow it wouldn't recgonize vectors so I put it in i,j,k format. $\endgroup$

Sep 16 '15 at 15:50
$\begingroup$ yep so I am getting 1 for both tangential and normal components. I hope I am right $\endgroup$

Sep 16 '15 at 15:56

$\begingroup$ Is that all the information you have ? What have you tried ? $\endgroup$

Sep 16 '15 at 15:38
$\begingroup$ so tangential acceleration seems like = V dot A / magnitude of V, so I dot product the acceleration and velocity the divide by magnitude of V which is 3. Am I right? The answer seems to be 1 for tangential acceleration $\endgroup$

Sep 16 '15 at 15:45
$\begingroup$ You are almost there. See answer posted by Onomnomnom $\endgroup$

Sep 16 '15 at 15:47
$\begingroup$ I fixed my question. Somehow it wouldn't recgonize vectors so I put it in i,j,k format. $\endgroup$

Sep 16 '15 at 15:50
$\begingroup$ yep so I am getting 1 for both tangential and normal components. I hope I am right $\endgroup$

Sep 16 '15 at 15:56

Accepted Answer

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The tangential component of $\vec a$ is given by $$ a_{tan} = \frac{\vec a \cdot \vec v}{\|\vec v\|} $$ The normal component is given by $$ a_{norm} = \left\|\vec a - \frac{a_{tan}}{\|\vec v\|}\vec v \right\| $$

answered Sep 16 '15 at 15:46

Ben GrossmannBen Grossmann

194k 12 gold badges 134 silver badges 271 bronze badges

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3

$\begingroup$ So I am getting an answer of 1 for both tangential and normal acceleration components. Am I right? I updated my question earlier, the main function wouldn't show which was: t=2 for: r(t)= t i + (t^2-1)/2 j + (t^2+1)/2 k or < t , (t^2 - 1)/2 , (t^2 + 1)/2 > $\endgroup$

Sep 16 '15 at 15:55
$\begingroup$ It looks like you're getting the right answer to me. $\endgroup$

Sep 16 '15 at 15:58
$\begingroup$ okay thank you so much! Thought so. $\endgroup$

Sep 16 '15 at 16:00