March 16th, 2017, 05:29 PM  #1 
Member Joined: Feb 2014 Posts: 91 Thanks: 1  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. 
March 16th, 2017, 06:08 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,342 Thanks: 984 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
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  
March 16th, 2017, 06:18 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
you've assumed the angle between the linear momentum and position vectors is 90 degrees ... it's not. $\theta = \arccos\bigg[\dfrac{\vec{r} \cdot \vec{v}}{\vec{r}\vec{v}}\bigg]$ $\vec{L} = \vec{r} \times m \vec{v} = \vec{r} \cdot m\vec{v} \sin{\theta}$ Last edited by skeeter; March 16th, 2017 at 06:50 PM. 
March 17th, 2017, 10:20 AM  #4 
Member Joined: Feb 2014 Posts: 91 Thanks: 1 
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. 
March 17th, 2017, 02:11 PM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
$\vec{r} \times m\vec{v}=9\begin{vmatrix} i & j & k\\ 8& 0& 4\\ 3 & 0 & 6 \end{vmatrix}=9\bigg[0\vec{i}(4812)\vec{j}+0\vec{k}\bigg]=324\vec{j}$ 
March 18th, 2017, 10:40 AM  #6 
Member Joined: Feb 2014 Posts: 91 Thanks: 1 
I hope I followed instruction correctly this time. Also cross product is way more complex than I thought. 
March 18th, 2017, 11:01 AM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
matrix calculations were not meant for humans to do by hand, imho ...

March 18th, 2017, 11:21 AM  #8 
Member Joined: Feb 2014 Posts: 91 Thanks: 1 
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.

March 18th, 2017, 12:25 PM  #9 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
$r = \sqrt{(8 )^2+4^2} = \sqrt{80} = 4\sqrt{5}$ $v = \sqrt{3^2+(6)^2} = \sqrt{45} = 3\sqrt{5}$ $r \, v = 60$ try again ... 
March 18th, 2017, 04:10 PM  #10 
Member Joined: Feb 2014 Posts: 91 Thanks: 1 
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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angular, determine, momentum 
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