3 Vectors in Physics 3 1 Scalars versus

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 …

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

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

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

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

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

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 A B A

• Adding Vectors: parallelogram method A C B • Adding Vectors Using Component Cx=Ax+Bx Cy=Ay+By Ex 1. A=3, 200 ; B=5, 450 C=?

Ex 2. C=? 2 300 600 3 Ex 3. A=2 m, θ=250; B=3 m, θ=600 Find | | and θ Ex 4. A= 3 m, θ=600, B=5 m , θ= - 1600 B A 600 200 1600

• Subtracting Vectors Dx=Ax-Bx Dy=Ax-By Ex 4. A= 10 m, 300; B=5 m, 600 Find , magnitude and direction ?