phy2048-ch3

phy2048-ch3 - 1 Chapter 3 Vectors I Definition II...

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Unformatted text preview: 1 Chapter 3 - Vectors I. Definition II. Arithmetic operations involving vectors A) Addition and subtraction - Graphical method- Analytical method b Vector components B) Multiplication Review of angle reference system Origin of angle reference system θ 1 0º< θ 1 <90º 90º< θ 2 <180º θ 2 180º< θ 3 <270º θ 3 θ 4 270º< θ 4 <360º 90º 180º 270º 0º Θ 4 =300º=-60º Angle origin 2 I. Definition Vector quantity: quantity with a magnitude and a direction. It can be represented by a vector. Examples : displacement, velocity, acceleration. Same displacement Displacement b does not describe the object’s path. Scalar quantity: quantity with magnitude, no direction. Examples : temperature, pressure Rules: ) 1 . 3 ( ) ( law e commutativ a b b a a a a a + = + ) 2 . 3 ( ) ( ) ( ) ( law e associativ c b a c b a a a a a a a + + = + + II. Arithmetic operations involving vectors- Geometrical method a a b a b a s a a a + = Vector addition: b a s a a a + = 3 Vector subtraction: ) 3 . 3 ( ) ( b a b a d a a a a a- + =- = Vector component: projection of the vector on an axis. θ θ sin ) 4 . 3 ( cos a a a a y x = = x y y x a a a a a = + = θ tan ) 5 . 3 ( 2 2 Vector magnitude Vector direction a of components Scalar a Unit vector: Vector with magnitude 1. No dimensions, no units. axes z y x of direction positive in vectors unit k j i , , ˆ , ˆ , ˆ → ) 6 . 3 ( ˆ ˆ j a i a a y x + = a Vector component- Analytical method: adding vectors by components. Vector addition: ) 7 . 3 ( ˆ ) ( ˆ ) ( j b a i b a b a r y y x x + + + = + = a a a 4 Vectors & Physics:-The relationships among vectors do not depend on the location of the origin of the coordinate system or on the orientation of the axes....
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phy2048-ch3 - 1 Chapter 3 Vectors I Definition II...

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