Where Did I Go Wrong? Solving for Angular Momentum in Air Table Puck Collision

In summary, the conversation discusses finding the distance from the center of mass (CoM) to the center of puck 1, denoted as y1, in symbolic form for part (a). The solution involves using the center of mass of each puck as the origin and calculating the vertical distance from the origin to the CoM of puck 2, denoted as r3. The final calculation for y1 is shown as y1 = (m2(r1+r2))/(m1+m2), and the correct notation for CoM is also clarified.
  • #1
ChiralSuperfields
1,322
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Homework Statement
Please see below
Relevant Equations
Please see below
For part(a),
1675366620399.png

The solution is,
1675370648471.png

However, I made a mistake somewhere in my working below and I'm not sure what it is. Does anybody please know? Thank you!

Here is a not too scale diagram at the moment of the collision,
1675366935512.png

## \vec L = \vec r \times \vec p ##
## \vec L = -y_{com}\hat j \times m_1v\hat i ##
## \vec L = y_{com}m_1v\hat k ##
## \vec L = \frac {m_2m_1v(r_1 +r_2)}{m_1 + m_2}\hat k ##
 

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  • #2
For part (a) please show what the distance ##y_1## from the CoM to the center of puck 1 is and how you got it in symbolic form.
 
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  • #3
kuruman said:
For part (a) please show what the distance ##y_1## from the CoM to the center of puck 1 is and how you got it in symbolic form.
Thank you for your reply @kuruman!

I assume that the COM of each puck is at the geometric center.

Choosing the center of ##m_1## as the origin where ##y = 0## and let ##r_3## be the vertical distance from ## y = 0## to the COM of ##m_2##.

## y_1 = y_{com} = \frac {m_1(0) + m_2r_3} {m_1 + m_2} ##

## y_1 = \frac {m_2(r_1 + r_2)} {m_1 + m_2} ##

Then substituting in values,

## y_1 = \frac {0.12(0.1)} {0.2} ##
## y_1 = 0.06 m ##

Also please see post #1, I missed some of the notations so I have edited it.

Many thanks!
 
  • #4
Thank you for your help @kuruman! I see now how they got their answer. I think I got confused because the solutions calculated the ##y_{com}## from a different point. Good idea to use ##y_1## notation for calculations of CoM with respect to different origins!Many thanks!
 

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