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Conservation of angular momentum (view source)

Revision as of 02:43, November 18, 2007

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== Example ==
 
== Example ==
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Imagine a rod of length l and mass M suspensed from one end vertically, and that a  mass having velocity v and mass m collides with the other end and sticks to it.  The maximum angle of displacement of the rod from the vertical axis can be calculated using the '''conservation of angular momentum''':
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Imagine a rod of length l and mass M suspensed from one end vertically, and that a  small block mass having velocity v and mass m collides with the other end and sticks to it.  The maximum angle of displacement of the rod from the vertical axis can be calculated using the '''conservation of angular momentum''':
    
:<math>\mathbf{L_i}=\mathbf{L_f}</math>  
 
:<math>\mathbf{L_i}=\mathbf{L_f}</math>  
    
:<math>\mathbf{m}\times{v}\times{l}= \mathbf{I}\times{\omega}</math>  
 
:<math>\mathbf{m}\times{v}\times{l}= \mathbf{I}\times{\omega}</math>  
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After the collision, there is conservation of energy such that the final potential energy of the rod (with the sticking block mass) equals the initial kinetic energy just after the collision:
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:<math>\mathbf{U_f}= \mathbf{KE_i}</math>
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Now solve the the two sides of the above equation separately:
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:<math>\mathbf{U_f}= \mathbf{U_{rod}}+\mathbf{U_{block}}</math>
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:<math>\mathbf{U_{rod}}= \frac{L}{2}\times(1-cos\theta)\times{M}\times{g}</math>
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[[category:physics]]
 
[[category:physics]]
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