Phys 325 Spring 2011 Lecture 23 - Physics 325 Lecture 23...

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Physics 325 Lecture 23 Newton’s 2 nd Law in a rotating reference frame We discussed several times now the important fact that Newton’s 2 nd law equation F ma is only valid in an inertial frame of reference. We showed in Lecture 21 that this equation is properly modified in a uniformly accelerating frame by adding to the right hand side a fictitious “inertial” force term mA , where A is the acceleration of the non- inertial frame as viewed in the inertial frame. We now do the same thing but for the general case of a non-inertial frame that may be translating and rotating with respect to an inertial frame. At the end of Lecture 21, we derived the following equation for the acceleration of an object as viewed from an inertial (“fixed”) frame: ( ) 2 f f r r a R a r r v   (23.1) As viewed by an observing in an inertial reference frame, we have the normal Newton’s Law equation: ( ) 2 f f r r F ma mR ma m r m r m v   (23.2) To an observer in the rotating coordinate system, however, the effective force eff F of a particle is given by (solving for r ma in Equation (23.2)) ( ) 2 eff r fr F ma F mR m r m r m v   (23.3) Let’s briefly describe each term in Equation (23.3). The 1 st term ( F ): net force acting on the particle as measured in the inertial frame 2 nd term ( f mR ): translational acceleration of non-inertial relative to inertial frame 3 rd term ( mr  ): rotational acceleration of non-inertial relative inertial frame 4 th term ( ()  ): the centrifugal force term 5 th term ( 2 r mv ): the Coriolis force term We have encountered the centrifugal force term several times before (e.g.
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Phys 325 Spring 2011 Lecture 23 - Physics 325 Lecture 23...

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