Lecture_8

# Lecture_8 - P123Lecture822October2010 Work,KineticEnergy...

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P123 Lecture 8 22 October 2010 Work, Kinetic Energy Review of Previous Lecture • Fluid resistance, terminal speed v at high speed Uniform circular motion D mg v mg f Dv f / 2  • Uniform circular motion Tangent to circle ; v = const Radially inward ; a = const v a a R a v 2 2 2 4 2 T R r T R R v r a v a  v • Particle of mass M undergoing uniform circular motion: Centripetal Force v R mv r F 2 r a R m 1 Object on Banked curve R

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VECTOR MULTIPLICATION : SCALAR PRODUCT B A A B A B B A B A Vector Addition: What does mean? B A B A B A Scalar Product (= Scalar) (projection of on ): B A A B A B A cos AB B A A B Note:   cos A B A B cos B B A A B  cos cos AB BA cos A B A 3 Scalar product of two vectors is COMMUTATIVE .

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SCALAR PRODUCT USING COMPONENTS Dot product is distributive C C B ) ( C B A C A B A A B cos B cos C Consider : j A i A A y x ˆ ˆ j B i B B x ˆ ˆ cos | | C B j ˆ i ˆ y ) ˆ ˆ ( ) ˆ ˆ ( j B i B j A i A B A y x y x j j B A i j B A j i B A i i B A x x ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1 ˆ ˆ ˆ ˆ j j i i 0 j i Use dot product to find angle between vectors y y x y y x ) ( z z y y x x B A B A B A         Use dot product to find angle between vectors.
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## This note was uploaded on 03/14/2011 for the course P 123 taught by Professor Stevens during the Spring '11 term at Rust.

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Lecture_8 - P123Lecture822October2010 Work,KineticEnergy...

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