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# lec15 - Physics 140 Fall 2007 lecture#15 25 Oct Ch 9 topics...

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Physics 140 – Fall 2007 lecture #15 : 25 Oct exam #2 is next Thursday, 1 November, 6:00-7:30pm • covers Chapters 6-8 • practice exam on CTools site -> Exams & Grading bring two 3x5 notecards, calculator, #2 pencils review next Monday evening, 29 Oct 182 Dennison 8:00-9:30pm Ch 9 topics: • rotational kinematics • rotational kinetic energy • moment of inertia Center of Mass of an extended, non-uniform object x com = 1 M dx dy " ( r ) x object ## y com = 1 M dx dy " ( r ) object ## y M = dx dy " ( r ) object ## x y An object with surface mass density ! ( r ), shown here in 2D, has a total mass given by the integral Its center of mass is defined by integrals of the mass-weighted positions:

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To describe rotational motion, we begin with the angular position " (in radians ) measured relative to an (arbitrary) reference angle. Rotational kinematics " 0 3 # /2 # # /2 really 2 n # , n =0,±1, ±2, ±3,… O A change in angular position, \$" , during a time interval \$ t implies a non-zero average angular velocity % avg = \$ " / \$ t A change in angular velocity, \$% , defines an average angular acceleration
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