9/2/2015PHY 711 Fall 2015 -- Lecture 41 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 4: Chapter 2 – Physics.

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9/2/2015PHY 711 Fall Lecture 41 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 4: Chapter 2 – Physics described in an accelerated coordinate frame 1.Linear acceleration 2.Angular acceleration 3.Foucault pendulum

9/2/2015PHY 711 Fall Lecture 42

9/2/2015PHY 711 Fall Lecture 4 3

9/2/2015PHY 711 Fall Lecture 44 Physical laws as described in non-inertial coordinate systems  Newton’s laws are formulated in an inertial frame of reference  For some problems, it is convenient to transform the the equations into a non-inertial coordinate system

9/2/2015PHY 711 Fall Lecture 45 Comparison of analysis in “inertial frame” versus “non- inertial frame”

9/2/2015PHY 711 Fall Lecture 46 Properties of the frame motion (rotation only): dd dd

9/2/2015PHY 711 Fall Lecture 47 Properties of the frame motion (rotation only): dd dd

9/2/2015PHY 711 Fall Lecture 48 Properties of the frame motion (rotation only): dd dd

9/2/2015PHY 711 Fall Lecture 49 Effects on acceleration (rotation only): Properties of the frame motion (rotation only) -- continued

9/2/2015PHY 711 Fall Lecture 410 Application of Newton’s laws in a coordinate system which has an angular velocity and linear acceleration Newton’s laws; Let r denote the position of particle of mass m: Coriolis force Centrifugal force

9/2/2015PHY 711 Fall Lecture 411 Motion on the surface of the Earth:

9/2/2015PHY 711 Fall Lecture 412 Non-inertial effects on effective gravitational “constant” 9.80 m/s m/s 2

9/2/2015PHY 711 Fall Lecture 413 Foucault pendulum The Foucault pendulum was displayed for many years in the Smithsonian's National Museum of American History. It is named for the French physicist Jean Foucault who first used it in 1851 to demonstrate the rotation of the earth.

9/2/2015PHY 711 Fall Lecture 414 Equation of motion on Earth’s surface  z (up) x (south) y (east) 

9/2/2015PHY 711 Fall Lecture 415 Foucault pendulum continued – keeping leading terms:

9/2/2015PHY 711 Fall Lecture 416 Foucault pendulum continued – keeping leading terms:

9/2/2015PHY 711 Fall Lecture 417 Foucault pendulum continued – coupled equations:

9/2/2015PHY 711 Fall Lecture 418 Foucault pendulum continued – coupled equations:

9/2/2015PHY 711 Fall Lecture 419

9/2/2015PHY 711 Fall Lecture 420 Summary of approximate solution for Foucault pendulum:

9/2/2015PHY 711 Fall Lecture 421  z (up) x (south) y (east) 