Summary : 3. Motion in 2- & 3-D

3.1. Vectors Vectors : Physics: Quantities with both magnitude & direction. 2. Mathematics : Members of a linear space. (Free vectors) Scalars: Quantities with only magnitude. Displacement Position vector Vector addition : Commutative : A + B = B + A 2. Associative : (A + B) + C = A + ( B + C )

A 2 A z y y x x Multiplication by scalar : Coordinate system. Cartesian coordinate system. A Az k = Az y k j A Ay = Ay j Ax i = Ax Ay j = Ay i y j  x x i Ax = Ax i Vector components: Unit vectors:

Vector Arithmetic with Unit Vectors Cartesian coordinate system : basis = rectilinear orthogonal unit vectors

2-D constant acceleration Projectile : ax = 0, ay = g

Uniform circular motion ( centripetal )  ( period )

Sailing Against the Wind