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PHY183-Lecture11 - Moving Reference Frames Origin of...

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January 26, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 11 January 26, 2006 Physics for Scientists&Engineers 1 2 Moving Reference Frames Moving Reference Frames ! Origin of coordinate system usually chosen for convenience Example: shift x 0 so that x 0 = 0 at start of projectile’s trajectory ! In examples so far coordinate system does not move ! But there are some situations for which a moving coordinate system is necessary Example: Airplane landing on a moving aircraft carrier January 26, 2006 Physics for Scientists&Engineers 1 3 Example: Airport Walkway Example: Airport Walkway ! Person walks with velocity v w , as measured by observer moving along with him on the walkway. ! Walkway surface moves with v wt relative to terminal. ! Two velocities add as vectors ! Velocity of person as measured by someone standing in the terminal: v t = v wt + v w January 26, 2006 Physics for Scientists&Engineers 1 4 Moving Reference Frames Moving Reference Frames ! Assume that reference frame (= coordinate system) moves with constant velocity relative to a 2 nd coordinate system that is at rest ! Then accelerations measured in both reference frames are the same ! Airport walkway example, again: If From we then obtain: v wt = const . ! dv wt / dt = 0 v t = v wt + v w dv t dt = d ( v wt + v w ) dt = dv wt dt + dv w dt = 0 + dv w dt ! a t = a w
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January 26, 2006 Physics for Scientists&Engineers 1 5 r r 3 Dimensions 3 Dimensions ! Consider two coordinate systems x,y,z and
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