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March 16th, 2017, 04:29 PM   #1
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Determine the angular momentum

Well finally got to the last question. I thought this one would be easy but I'm unsure. I've looked into this question. I have the mass, the velocity, and I think radius. If I manage to get the last one right that would be awesome.



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March 16th, 2017, 05:08 PM   #2
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Originally Posted by The_Ys_Guy View Post
Well finally got to the last question. I thought this one would be easy but I'm unsure. I've looked into this question. I have the mass, the velocity, and I think radius. If I manage to get the last one right that would be awesome.



The formula for angular momentum is $\displaystyle \vec{L} = m \vec{r} \times \vec{v} = m |v| |r| ~ sin(\theta)$
where $\displaystyle \theta$ is the angle between $\displaystyle \vec{r}$ and $\displaystyle \vec{v}$.

How do you find that angle? (Hint: Use the definition of the cross product.)

-Dan
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March 16th, 2017, 05:18 PM   #3
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you've assumed the angle between the linear momentum and position vectors is 90 degrees ... it's not.

$\theta = \arccos\bigg[\dfrac{\vec{r} \cdot \vec{v}}{|\vec{r}||\vec{v}|}\bigg]$

$\vec{L} = \vec{r} \times m \vec{v} = |\vec{r}| \cdot m|\vec{v}| \sin{\theta}$
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Last edited by skeeter; March 16th, 2017 at 05:50 PM.
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March 17th, 2017, 09:20 AM   #4
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Okay here is attempt two. I look all over the web to find anything I could and I think I got it right. It appears the cross product of vectors with only 2 dimension is the determinent. The cross product definition had an n variable at the end.

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March 17th, 2017, 01:11 PM   #5
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$\vec{r} \times m\vec{v}=9\begin{vmatrix}
i & j & k\\
-8& 0& 4\\
3 & 0 & -6
\end{vmatrix}=9\bigg[0\vec{i}-(48-12)\vec{j}+0\vec{k}\bigg]=-324\vec{j}$
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March 18th, 2017, 09:40 AM   #6
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I hope I followed instruction correctly this time. Also cross product is way more complex than I thought.

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March 18th, 2017, 10:01 AM   #7
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matrix calculations were not meant for humans to do by hand, imho ...
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March 18th, 2017, 10:21 AM   #8
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Did I finally calculate theta right? I'll look up the matrix functionality of my calculator but I really need to know if I'm on the right path.
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March 18th, 2017, 11:25 AM   #9
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$|r| = \sqrt{(-8 )^2+4^2} = \sqrt{80} = 4\sqrt{5}$

$|v| = \sqrt{3^2+(-6)^2} = \sqrt{45} = 3\sqrt{5}$

$|r| \, |v| = 60$

try again ...
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March 18th, 2017, 03:10 PM   #10
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this is depressing now.....I really hope there aren't a lot of these on the next test. Please tell me I got it this time.



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