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Conservation of angular momentum (view source)

Revision as of 03:37, November 18, 2007

314 bytes added ,  03:37, November 18, 2007
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An ordinary rod of length ''l'' has the following moment of inertia relative to an axis of rotation at one end:
 
An ordinary rod of length ''l'' has the following moment of inertia relative to an axis of rotation at one end:
   −
:<math>I \ \stackrel{\mathrm{def}}{=}\  \sum_{i=1}^{N} {m_{i} r_{i}^2}\,\!</math>
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:<math>\mathbf{I}= \frac{M}{3}\times{l^2}</math>  
    
A [[moment of inertia]] is additive, defined as follows:
 
A [[moment of inertia]] is additive, defined as follows:
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::<math>I \ \stackrel{\mathrm{def}}{=}\  \sum_{i=1}^{N} {m_{i} r_{i}^2}\,\!</math>
 
::<math>I \ \stackrel{\mathrm{def}}{=}\  \sum_{i=1}^{N} {m_{i} r_{i}^2}\,\!</math>
 
where ''m'' is the mass at each (perpendicular) distance ''r'' from the axis of rotation.
 
where ''m'' is the mass at each (perpendicular) distance ''r'' from the axis of rotation.
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Thus the the moment of inertia ''I'' for a rod of length ''l'' and mass ''M'', with a small block of mass ''m'' at its end is simply this:
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:<math>\mathbf{I}= \frac{M}{3}\times{l^2} + 3m\times{l^2}</math>
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which is:
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:<math>\mathbf{I}= \frac{1}{3}\times(3m+M)\times{l^2}</math>
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Plugging this back into the unsolved equation above yields:
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[[category:physics]]
 
[[category:physics]]
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