Lecture 13 - Gyroscopes

Lecture 13 - Gyroscopes - ur ur Precession is generally not...

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Gyroscopes
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Bicycle wheel on a rope into the plane Spin the bicycle wheel into the plane c dL r F dt L I dL dt τ ϖ = × = = = ur r r ur ur ur ur r
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Rate of precession d dt dL dt φ τ Ω = = ur r
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( 29 c c dr v r dt d dt dL L dt mga I mga I ϖ τ = = = = Ω = Ω Ω = r r r ur r
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2 constant = 0 Balanced by dropping KE of precession z z L L M a U = = =
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( 29 ( 29 ( 29 2 2 2 2 2 2 precession drop 1 nutation 2 z z c L a M h L I a gh a v mgh Mv Mv ϖ = = = Ω = = = +
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Three separate motions : spin , angular momentum : precession Nutation: another frequency L I ϖ =
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Unformatted text preview: ur ur Precession is generally not in the horizontal plane. Gyroscope equation d dt dL dt L τ → Ω× = = Ω× ur r r ur ur sin sin Still true. c L L r F aMg Mga I β ϖ Ω× = Ω × = Ω = ur ur r ur Worst gyroscope = bicycle wheel Best gyroscope: Maximize Minimize Reduce c Mga L I I M a g τ ϖ Ω = =...
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This note was uploaded on 11/20/2009 for the course PH ASF taught by Professor Goodstein during the Spring '07 term at Caltech.

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Lecture 13 - Gyroscopes - ur ur Precession is generally not...

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