3 Vectors in Physics 3-1 Scalars versus Vectors Scalar: a number with unit volume, time, temperature, distance … Vector: a mathematical quantity with both direction and magnitude velocity, acceleration, displacement …

Vector: draw diagram or sketch Magnitude: length of line Direction: arrow (2) Vector: write Boldface, r Draw arrow over the vector’s symbol Magnitude: r=|r|=| | θ x y r

3-2 The component of vector Resolve or decompose vector on the x and y axis θ x y r rx ry θ Hypotenuse (H) Opposite (O) Adjacent (A)

II x -, y+ sin +, cos -, tan - 900<ϴ<1800 I Quadrant x +, y+ sin +, cos +, tan + 0<ϴ<900 1800 -α α III x -, y- sin -, cos -, tan + 1800<ϴ<2700 IV x +, y - sin -, cos +, tan - 2700<ϴ<3600 1800 +α 3600 –α or -α

Ex1. O=?, H=? O=? 2 300 400 3 A O O=?, A=? θ=?, O=? Θ=? 2 1

Ex2. Say you walk 3 m right and 11 m north, find the magnitude and direction of displacement. Ex3 θ O x y -2m -1 m r=?, θ=?

3-2 Adding and Subtracting Vectors Adding vectors Graphically Connect vector head and tail, the sum vector is free tail to point free head C D B C B A A

Adding Vectors: parallelogram method Adding Vectors Using Component Cx=Ax+Bx Cy=Ay+By Ex1. A=3, 200 ; B=5, 450 C=? A C B

Ex2. C=? Ex3. A=2 m, θ=250; B=3 m, θ=600 Find | | and θ Ex4. 300 600 2 3 Ex2. C=? Ex3. A=2 m, θ=250; B=3 m, θ=600 Find | | and θ Ex4. A= 3 m, θ=600, B=5 m , θ= - 1600 600 1600 200 A B

Subtracting Vectors Dx=Ax-Bx Dy=Ax-By Ex4. A= 10 m, 300; B=5 m, 600 Find , magnitude and direction ?