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homework7_answers - Homework Problem Set#7 ATOC/ASEN 5235...

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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 ω 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 ω Equation 9.12: ) 1 ( + = J J L h Therefore, I J J ) 1 ( + = h ω For adjacent quantum numbers, [ ] ) 1 ( ) 2 )( 1 ( 1 2 + − + + = − J J J J I h ω ω The largest possible value of Δω would occur for J=0, so I / 2 h = Δ ω Therefore, if I is very large compared to h , then Δ ω ~ 0 and the motion will appear to be continuous (not quantized). Consider actual numbers: π 2 / 2 h = 6.626 × 10-34 2 1/2 / 2 π = 1.49 × 10-34 J s I = μ r 2 . If μ = 0.1 kg and r = 0.1 m then I = 10-3 kg m 2 so: 31 3 34 10 49 . 1 10 / 10 49 . 1 − − − × = × = Δ ω s-1 . This is far too small to be observed....
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homework7_answers - Homework Problem Set#7 ATOC/ASEN 5235...

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