7lecture2a08

7lecture2a08 - Physics 2A Lecture 7: Jan 23 Vivek Sharma...

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Physics 2A Lecture 7: Jan 23 Vivek Sharma UCSD Physics
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Generalizing Motion From 1D 3D Cartesian coordinate system in 3D 11 1 1 2 222 21 1 When particle moves f ˆ ˆˆ Position Vector rom P (x rx y z Path of particle moving in 3D spac ,y ,z ) P (x ,y ,z ) ˆ displacement r = e is a curve (x -x ) (y -y ) z -z ) =+ Δ+ 2 i j+( k ij + k G G ˆ x y z Δ Δ = i j+ k
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Velocity in 3 Dimensions 21 av Average Velocity Vector rr r V tt t −Δ == GG G G t0 at every point along the path, Instant. Velocity Vector rd r V l vector V is tangent to the path im td t at that point Δ→ Δ Δ G G
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Components of Velocity Vector xy z 222 x y z ˆ ˆˆ v v dr dx dy dz ˆ dt dt v Speed = v dt = |v| = v v dt v == + + + + i j + i j +k k = G G G 22 y x v Speed = v dx dy = |v| = v v v tan v dt dt dt + =+ + α= = ij = j G G G In 2 dimensions
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Acceleration In 3 Dimension 21 Vector subtraction v = v v Δ− GG G av Average Acceleration vv v a tt t −Δ == G G 2 2 t0 a always points towards the side of the c Instantaneous Acceleration vd r al i m td t When moving in a cur u v rv ed ed p path even if speed is consta t 0 th n a a Δ→ Δ = Δ concave G G G G
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Components of Acceleration Vector 22 xy 2 xz z y 2 ˆ ˆˆ a a dv dv dv ˆ dx dy dz ˆ dt dt d td t d t dt a =+ + + ij i j + +k + k = = k G When computing components use the correct def. of angle
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3D Motion With Constant Acceleration 22 0 0 0 2 0 0 0 0 1 | 2 2 2| rr v t a t v vv a r r v va t v t =+ + ⎛⎞ + = + = GG G G G G G G G
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and components of Acceleration a G & When moving in curved path useful to describe acceleration a in terms of components which are &v to G G & φ a = a a with |a|co s | a | s i W n rite + & & G G GG G
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and components of Vector a G & When a v or anti- vector addition change in magnitude of but not its direc n v tio G G && G When a v vector addition change the direction o but not its magnitude (speed remains unch f anged ) v !
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7lecture2a08 - Physics 2A Lecture 7: Jan 23 Vivek Sharma...

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