PHY 107 1st Edition Lecture 8 Outline of Last Lecture I. Free fall motion - “Round trip” free fallII. Graphical integration in motion analysis (non-constant acceleration)Outline of Current Lecture III. Galilean TransformationIV. Relative Motion in One DimensionV. Relative Motion in Two DimensionsCurrent LectureGalilean Transformation – equations that connect the velocities seen by two different observers- The velocity of a particle, P, determined by 2 different observers, A and B, varies from observer to observer.Relative Motion in One Dimension:- The velocity of a particle, P, determined by 2 different observers, A and B, varies from observer to observer.- Relative motion – observers moving with respect to each other will describe motion differently - Transformation equation of velocities – gives exact relationship between the velocities each observer perceives o Assume observer B moves with a known, constant velocity (vBA) with respect to observer A- Observers A and B determine the coordinates of particle P to be xA and xB, respectively- xA = xB + xBA → ddt(xA) = ddt(xB) + ddt(xBA) → vA = vB + vBA-d vBAdt = 0 → aA = aB (even though the observers measure different velocities for P, they measure the same acceleration)Relative Motion in Two Dimensions:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- The velocity of a particle, P, determined by 2 different observers, A and B, varies from observer to observer.- Assume observer B moves with constant velocity (vBA) with respect to observer A in the xy plane- Observers A and B determine the position vector of particle P to be ´rA and ´rB, respectively -´rA = ´rB + ´rBA → ddt´rA = ddt´rB + ddt´rBA → ´vA = ´vB + ´vBA -ddt´vA = ddt´vB + ddt´vBA → d vBAdt = 0 → ´aA = ´aB (even though the observers measure different velocities for P, they measure the same
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