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Unformatted text preview: Kinematics General Physics I Mechanics Racquetball Striking a Wall in 3D Physics 140 Mt. Etna Stewart Hall Description of motion in 3D • Choose a coordinate system; choose its origin • The position vector r is from the origin to the cation of an object (a location of an object (a point) • The position vector can be written in components: k z j y i x r ˆ ˆ ˆ + + = r Description of motion in 3D • As the object moves, the position vector changes with time ach component • Each component of vector r is now a function of time • Displacement vector: 1 2 r r r r r r = ∆ Velocity in 3D • Average velocity: • Instantaneous t r t t r r v aver ∆ ∆ = = r r r r 1 2 1 2 velocity: • Time derivative of the position vector dt r d t r v t r r r = ∆ ∆ = → ∆ lim Velocity in 3D • Instantaneous velocity: ( 29 z y x k z j y i x dt d dt r d v ˆ ˆ ˆ + + = = r r • Velocity components k dt dz j dt dy i dt dx ˆ ˆ ˆ + + = dt dz v dt dy v dt dx v z y x = = = Acceleration in 3D • If the velocity vector changes (in magnitude or in direction), there is acceleration • Average acceleration: t v t t v v a aver ∆ ∆ = = r r r...
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This note was uploaded on 02/15/2012 for the course PHYS 140 taught by Professor Uher during the Winter '10 term at University of Michigan.
 Winter '10
 Uher
 mechanics

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