Extended_Angular_Momentum_Principle

Extended_Angular_Momentum_Principle - AN EXTENSION OF THE...

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AN EXTENSION OF THE ANGULAR MOMENTUM PRINCIPLE FOR SUMMING MOMENTS ABOUT ANY POINT Consider what the angular momentum principle would look like if we summed moments for any body B about ANY point O : / ? / NN B O BO d dt = H M Of course, we know that this equation holds true IF AND ONLY IF point O is selected as either the mass center Bcm of the body or a point No fixed in N . From the shift theorem for angular momentum, we know that // / NB O NB B c m B c m ONB =+ × HH p L Consequently, / / () O N B c m B c m B c m N B c m O NNB B c m O dd dt dt d dt dt dt × × + × H Hp L L Lp Consider what happens to this expression when we pick point O as either the mass center Bcm or a point No fixed in N . If point O is chosen as the mass center Bcm , then O NN B B c m dt dt = while if point O is chosen as a point No fixed in N , then / B c m Bcm No d dt dt dt × L p However, if point O is chosen as any other point, then the original expression for / / O t H contains an extra term / / c m O N B t × pL that makes / / O d dt H
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Extended_Angular_Momentum_Principle - AN EXTENSION OF THE...

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