Why Does the Derivative of Momentum Appear in Angular Momentum Calculations?

AI Thread Summary
The discussion centers on the confusion regarding the appearance of the derivative of momentum in the derivation of the angular momentum theorem for a system of particles. The user initially struggles to understand why the difference in velocities leads to the derivative of momentum rather than just momentum itself. After some reflection, they realize that differentiating the expression clarifies the concept. However, they encounter further confusion with an additional term that appears during differentiation. Ultimately, they express relief at resolving their misunderstanding and consider taking a break from studying.
Xyius
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I do not understand this one step in deriving the angular momentum theorem for a system of particles.

The vector angular momentum about the point Q, not necessarily the origin is..
[PLAIN]http://img27.imageshack.us/img27/8196/pfquestion.gif

I do not understand why the difference in the velocities of the point Q and k equals the DERIVATIVE of the momentum. If you bring the mass term into the expression, then shouldn't it be equal to just p? Why is it dp/dt??
 
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Never mind, I just got it by differentiating. Now what I don't get is the next part. I will post a pic soon.

EDIT:
Okay so, when I differentiate the expression for angular momentum, I get the expression above. When THEY differentiate it, they get what I have plus this additional term.

[PLAIN]http://img24.imageshack.us/img24/9514/pfquestion1.gif

Maybe I am being oblivious again, but I cannot get this term to make sense!
 
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Yup! being oblivious again! I got it. I think on that note, I should finally stop studying haha.
 

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