Ch10 - PHY126 Summer Session I, 2008 Most of information is...

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PHY126 Summer Session I, 2008 • Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY126-08 including the syllabus and lecture slides. Read syllabus and watch for important announcements. • Homework assignment for each chapter due nominally a week later. But at least for the first two homework assignments, you will have more time. All the assignments will be done through MasteringPhysics, so you need to purchase the permit to use it. Some numerical values in some problems will be randomized. • In addition to homework problems and quizzes, there is a reading requirement of each chapter, which is very important.
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Chapter 10: Rotational Motion Movement of points in a rigid body ± All points in a rigid body move in circles about the axis of rotation z y x P Axis of rotation orbit of point P A rigid body has a perfectly definite and unchanging shape and size. Relative position of points in the body do not change relative to one another. In this specific example on the left, the axis of rotation is the z-axis. rigid body
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Movement of points in a rigid body (cont’d) ± At any given time, the 2-d projection of any point in the object is described by two coordinates ( r , θ ) In our example, 2-d projection onto the x-y plane is the right one. y P x r θ s = r θ where s,r in m, and θ in rad(ian) length of the arc from the x-axis s: A complete circle: s = r 360 o = 2 π rad 57.3 o = 1 rad 1 rev/s = 2 π rad/s 1 rev/min = 1 rpm
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Angular displacement, velocity and acceleration ± At any given time, the 2-d projection of any point in the object is described by two coordinates ( r , θ ) y Angular displacement: ∆θ = θ 2 −θ 1 in a time interval t=t 2 –t 1 P at t 2 Average angular velocity: 1 2 1 2 t t t avg = = θ ω r rad/s θ 2 θ 1 P at t 1 Instantaneous angular velocity: dt d t t = = 0 lim x rad/s ω < (>) 0 ( counter) clockwise rotation
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Angular displacement, velocity and acceleration (cont’d) ± At any given time, the 2-d projection of any point in the object is described by two coordinates ( r , θ ) y x P at t 2 r θ 2 θ 1 P at t 1 Average angular acceleration: Instantaneous angular acceleration: 1 2 1 2 t t t avg = = ω α rad/s 2 dt d t t = = 0 lim rad/s 2
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Correspondence between linear & angular quantities Linear Angular Displacement Velocity Acceleration x θ dt dx v / = dt d / ω= dt dv a / = dt d / ω α=
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Case for constant acceleration (2-d) ± Consider an object rotating with constant angular acceleration α 0 0 / α ω = = dt d = t t dt dt dt d 0 0 0 ) / ( = 0 0 t d t 0 0 = t 0 0 + = + = = t t t t dt t dt dt d dt dt d 0 0 0 0 0 ) / ( ) / ( θ 2 0 0 0 ) 2 / 1 ( t t + = 2 0 0 0 ) 2 / 1 ( t t + + = Eq.(1) Eq.(2)
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Ch10 - PHY126 Summer Session I, 2008 Most of information is...

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