PHY183-Lecture08pre-2

PHY183-Lecture08pre-2 - Three Dimensional Coordinate...

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1 January 23, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 201 Lecture 8 Motion in Two and Three Dimensions Three Dimensional Coordinate Systems Now we move from one dimensional motion to motion in two and three dimensions We will work in Cartesian coordinates January 23, 2012 Physics for Scientists&Engineers 1 2 Right Handed Coordinate System January 23, 2012 Physics for Scientists&Engineers 1 3 Position, Velocity, Acceleration in 3D We can write the position vector as We can write the velocity vector as We can write the acceleration vector as January 23, 2012 Physics for Scientists&Engineers 1 4 r = ( x , y , z ) = x ˆ x + y ˆ y + z ˆ z v = ( v x , v y , v z ) = v x ˆ x + v y ˆ y + v z ˆ z a = ( a x , a y , a z ) = a x ˆ x + a y ˆ y + a z ˆ z v x = dx dt v y = dy dt v z = dz dt a x = dv x dt a y = dv y dt a z = dv z dt 222 xyz dx dy dz aaa dt dt dt === January 23, 2012 Physics for Scientists&Engineers 1 5 Velocity and Acceleration in a Plane A striking difference between velocity along a line and velocity in two or more dimensions is that velocity can change direction as well as magnitude Any change in velocity produces acceleration, even when the magnitude of the velocity does not change a ave = Δ v Δ t = v 2 v 1 t 2 t 1 v 2 > v 1 v 2 and v 1 same direction v 2 < v 1 v 2 and v 1 same direction v 2 = v 1 v 2 and v 1 different directions In some special cases of 3D motion, the horizontal projection of the flight path is a straight line Accelerations in x and y directions are zero v and are constant In this special case, the motion in three dimensions can be described as motion in two dimensions
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This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture08pre-2 - Three Dimensional Coordinate...

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