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Unformatted text preview: Homework Problem Set #7 ATOC/ASEN 5235, Fall 2010 Due Tuesday, 30 November 1. (20 points). Petty Problem 9.2. Equations 9.11 and 9.12 imply that the angular velocity of an object can only take on discrete (quantized) values. Explain why this quantization is not observable for macroscopic objects like frisbees and hula hoops. Your explanation should be quantitative , not just qualitative! Answer : Equation 9.11: L = I Equation 9.12: ) 1 ( + = J J L h Therefore, I J J ) 1 ( + = h For adjacent quantum numbers, [ ] ) 1 ( ) 2 )( 1 ( 1 2 + + + = J J J J I h The largest possible value of would occur for J=0, so I / 2 h = Therefore, if I is very large compared to h , then ~ 0 and the motion will appear to be continuous (not quantized). Consider actual numbers: 2 / 2 h = 6.626 1034 2 1/2 / 2 = 1.49 1034 J s I = r 2 . If = 0.1 kg and r = 0.1 m then I = 103 kg m 2 so: 31 3 34 10 49 . 1 10 / 10 49 . 1 = = s1 . This is far too small to be observed....
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 Fall '10
 Randell

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