CM and Momentum

CM and Momentum - Center of Mass and Momentum PHYS116A02...

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Center of Mass and Momentum PHYS-116A-02, 9/30/10,  Lecture 11 Momchil Velkovsky

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Center of mass 1 2 Pull out the total mass ( ) n m m m + + L 1 1 2 2 Weighted sum: n n m r m r m r + + = r r r L com r r x y m 1 m 2 m 3 m 4 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 1 2 , in components: , , , For two particles: , if , 2 , 2 n n com n n n n n n com com com com com m r m r m r r M m x m x m x m y m y m y m z m z m z x y z M M M m x m x x x x m m m M m x M + + = + + + + + + = = = + + = = = = = r r r L r L L L
Solid bodies, composite bodies

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Center of mass surprises
Why? Justification of everything we did up to now 1 1 2 2 1 1 2 2 1 1 2 2 1 2 1 1 2/1 3/1 /1 1 2 , , , , , com n n com n n com n n com n ext n com ext ext next net Mr m r m r m r Mv m v m v m v Ma m a m a m a Ma F F F F F F F F Ma F F F F = + + = + + = + + = + + = + + + + = + + = r r r r L r r r r L r r r r L r r r r L r r r r r L r r r r r L

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Tug-of-war without friction (on the feet)
How does momentum relate to mass and velocity? 1 2 Newton's Second law in another form , , . For a system , net net n dp dv p mv m ma F dt dt dp F dt p p p p = = = = = = + + + r r r r r r r r r r r r L Remember d , , summing Imp p ulse u f i t f i t W F dr dp dJ Fdt dt dp dt J Fdt p p p = = = = = = ∆ ≡ - r r g r r r r r r r r r

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The impulse–momentum  relationship depends on
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CM and Momentum - Center of Mass and Momentum PHYS116A02...

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