lec_week14

lec_week14 - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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± 18.02 Lecture 33. Thu, Dec 6, 2007 Handouts: PS12 solutions; exam 4 solutions; review sheet and practice fnal. Applications of div and curl to physics. Recall: curl oF velocity feld = 2 angular velocity vector (oF the rotation component oF motion). · E.g., For uniForm rotation about z -axis, v = ω ( y ˆ ı + x ˆ j ), and × v = 2 ω k ˆ . Curl singles out the rotation component oF motion (while div singles out the stretching compo± nent). Interpretation of curl for force Felds. IF we have a solid in a Force feld (or rather an acceleration feld!) ± such that the Force exerted on Δ m at ( x, y, z ) is ± ( x, y, z ) Δ m : recall the torque oF the Force about the origin is defned as τ = r × ± (For the entire solid, take . . . δ dV ), and measures how ± imparts rotation motion.
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This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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lec_week14 - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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