apr04a - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.055 / Art of approximation 56 The other possibility is to add quantum mechanics, which was developed to solve funda- mental problems like the existence of matter. The physics of quantum mechanics is com- plicated, but its effect on dimensional analyses is simple: It contributes a new constant of nature ~ whose dimensions are those of angular momentum. Angular momentum is mvr , so [ ~ ] = ML 2 T − 1 . The ~ might save the day. There are now two quantities Var Dim What containing time dimensions. Since e 2 / 4 π 0 has T − 2 and a 0 L size ~ has T − 1 , the ratio ~ 2 / ( e 2 / 4 π ) contains no time dimen- e 2 / 4 π 0 ML 3 T − 2 sions. Since m e M electron mass " ~ 2 # ~ ML 2 T − 1 quantum = ML , e 2 / 4 π 0 a dimensionless group is ~ 2 a m e ( e 2 / 4 π ) It turns out that all dimensionless groups can be formed from this group. So, as in the It turns out that all dimensionless groups can be formed from this group....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.

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apr04a - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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