W9.1 - March 10, 2008 Physics for Scientists&Engineers...

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Unformatted text preview: March 10, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Lecture 31 March 10, 2008 Physics for Scientists&Engineers 1 2 Angular Velocity Angular Velocity Linear motion: rate of change of displacement is velocity Angular motion: rate of change of angular displacement is angular velocity • Average: • Instantaneous: Unit: Direction: right-hand rule ! = " 2 #" 1 t 2 # t 1 = $" $ t ! = lim " t # ! = d $ dt ! [ ] = March 10, 2008 Physics for Scientists&Engineers 1 2 Angular Velocity Angular Velocity Linear motion: rate of change of displacement is velocity Angular motion: rate of change of angular displacement is angular velocity • Average: • Instantaneous: Unit: Direction: right-hand rule ! = " 2 #" 1 t 2 # t 1 = $" $ t ! = lim " t # ! = d $ dt ! [ ] = rad/s March 10, 2008 Physics for Scientists&Engineers 1 3 Frequency Frequency Frequency, f , measures numbers of turns around the circle Example: rpm on tachometer Since 1 turn = 2 π radians: Unit: [ f ]=1/s In honor of Heinrich Rudolf Hertz (1857-1894): 1/s = 1 Hz Period, T : Relationship with angular velocity: f = ! 2 " #! = 2 " f T = 1 f ! = 2 " f = 2 " T T = 2 ! " March 10, 2008 Physics for Scientists&Engineers 1 4 Linear and Angular Velocity Linear and Angular Velocity Write r in Cartesian coordinates, then use transformation to polar coordinates and take derivatives (remember: r = const ., and d θ /dt = ω ) Result: linear velocity vector points in tangential direction Magnitude: !...
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This note was uploaded on 04/06/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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W9.1 - March 10, 2008 Physics for Scientists&Engineers...

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