L8F11 - P123F11Lecture821October2011 Work,KineticEnergy...

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1 P123F11 Lecture 8 21 October 2011 Work, Kinetic Energy Review of Previous Lecture • Fluid resistance, terminal speed at high speed • Uniform circular motion • Particle of mass M undergoing uniform circular motion: Centripetal Force Object on Banked curve Tangent to circle ; v = const Radially inward ; a = const v D mg v mg f Dv f / 2  v a a v 2 2 2 4 2 T R r T R R v r a v a R mv r F 2  a v R r a v R m R
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2 i Clicker T v
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3 VECTOR MULTIPLICATION: SCALAR PRODUCT Vector Addition: What does mean? Scalar Product (= Scalar) (projection of on ): Note: Scalar product of two vectors is COMMUTATIVE. B A B A B A B A cos AB B A A B A B A B A A B    cos cos cos AB BA A B A B A B A B A B B A B A A B cos B cos A B A
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4 SCALAR PRODUCT USING COMPONENTS Dot product is distributive Consider : Use dot product to find angle between vectors. Example : ) ( C B A C A B A j A i A A y x ˆ ˆ j B i B B y x ˆ ˆ ) 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 y y x y y x x x ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ) ( z z y y x x B A B A B A cos | | C B j ˆ 1 ˆ ˆ ˆ ˆ j j i i 0 ˆ ˆ
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This note was uploaded on 01/03/2012 for the course PHYSICS 750:123 taught by Professor Ronaldgilman during the Fall '11 term at Rutgers.

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L8F11 - P123F11Lecture821October2011 Work,KineticEnergy...

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