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W2.4 - Physics for Scientists Engineers 1 Spring Semester...

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January 11, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 8
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January 11, 2008 Physics for Scientists&Engineers 1 2 Motion in 1 Dimension Motion in 1 Dimension First case: simple linear motion Special case 1: motion with 0 acceleration Special case 2: motion with constant acceleration 2a: Free fall with a=-g Other cases for later: 1) Circular motion Motion in a 2-dimensional plane 2D motion reducible to 1D motion by introducing new set of coordinates in the plane (polar coordinates). 2) Oscillations of an object attached to a spring Motion due to force that is proportional to displacement = “Restoring force”
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January 11, 2008 Physics for Scientists&Engineers 1 3 Coordinate System Coordinate System In general, we use a 3-dimensional Cartesian coordinate system, with x-, y-, and z-axis Coordinate system has to be Orthogonal: 90° angles between each pair of axes Right-handed
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January 11, 2008 Physics for Scientists&Engineers 1 4 Working in Components Working in Components Position vector Velocity vector Acceleration vector ! 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
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January 11, 2008 Physics for Scientists&Engineers 1 5 Projectile Motion Projectile Motion
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