LectureNotes03 - Copyright R. Janow Spring 2012 Physics 111...

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Unformatted text preview: Copyright R. Janow Spring 2012 Physics 111 Lecture 03 Motion in Two Dimensions SJ 8th Ed.: Ch. 4.1 4.4 Position, velocity, acceleration vectors Average & Instantaneous Velocity Average & Instantaneous Acceleration Two Dimensional Motion with Constant Acceleration (Kinematics) Projectile Motion (Free Fall) Uniform Circular Motion Tangential and Radial Acceleration Relative Velocity and Relative Acceleration 4.1 Position, Velocity and Acceleration Vectors 4.2 Two Dimensional Motion with Constant Acceleration 4.3 Projectile Motion 4.4 A particle in Uniform Circular Motion 4.5 Tangential and Radial Acceleration 4.6 Relative Velocity and Relative Acceleration Copyright R. Janow Spring 2012 Motion in two and Three Dimensions Extend 1 dimensional kinematics to 2 D and 3 D n descriptio z y, x, or y x, x Kinematic quantities become 3 dimensional k z j y i x r x + + r k v j v i v v v z y x + + r k a j a i a a a z y x + + r Motions in the 3 perpendicular directions can be analyzed independently Vectors needed to manipulate quantities Constant acceleration Kinematic Equations hold component-wise for each dimension t a v v x x0 x + = 2 x 2 1 x0 t a t v x x + =- ) x (x 2a v v x 2 x0 2 x- + = t a v v y y0 y + = 2 y 2 1 y0 t a t v y y + =- ) y (y 2a v v y 2 y0 2 y- + = Same for z In vector notation each equation is 3 separate ones for x, y, z t a v v r r r + = 2 2 1 t a t v r r r r v r + =- z y, ) x (x 2a v v for same & x 2 x0 2 x- + = Copyright R. Janow Spring 2012 Position and Displacement A particle moves along its path as time increases r r r i f r r r- Displacement Positions Trajectory: y = f(x) Parameterized by time j ] y [y i ] x [x j y i x r i f i f- +- = + = r f i f f i i t t ) (t r r ) (t r r < r r r r always points from the origin to the particles location r r Path does not show time dependence. Slopes of (tangents to) x(t), y(t), z(t) graphs would show velocity components Average Velocity t r interval time nt displaceme v avg = r r Same direction as r r Rate of change of position Copyright R. Janow Spring 2012 Instantaneous Velocity j v i v dt r d t r Lim t ) v ( Lim t v y x avg + = = r r r r dt dy v dt dx v y x where x y v r parabolic path Free Fall Example is tangent to the path in x,y i.e, to a plot of y vsx v r slope v x = t x t v ) t ( x x = t y y(t) is parabolic 2 t g 2 1- t v- ) t ( y y0 = Components of are tangent to graphs of corresponding components of the motion, viz: v r v x is tangent to x(t) v y is tangent to y(t) Copyright R. Janow Spring 2012 Displacement in 3 Dimensions k z j y i x r i i i i + + r k z j y i x r + + = r r r r i f r r r- f r r r i r r r k v j v i v t r Lim t ) v ( Lim t v z y x avg r r r r + + = = Copyright R. Janow Spring 2012Copyright R....
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This note was uploaded on 03/02/2012 for the course PHYS 17328 taught by Professor Darilpedigo during the Spring '09 term at University of Washington.

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LectureNotes03 - Copyright R. Janow Spring 2012 Physics 111...

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