3 Vectors in Physics3-1 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

(2) Vector: write

Boldface, r

Draw arrow over the vector’s symbol

Magnitude: r=|r|=| |

θ

x

y

r

r

r

3-2 The component of vector

Resolve or decompose vector on the x and y axis

θ

Hypotenuse (H)

Opposite (O

)

Adjacent (A)

θ

x

y

r

rx

ry

sinrry cosrrx

I Quadrantx +, y+sin +, cos +, tan +0<ϴ<900

IIx -, y+sin +, cos -, tan -900<ϴ<1800

IIIx -, y-sin -, cos -, tan +1800<ϴ<2700

IVx +, y -sin -, cos +, tan -2700<ϴ<3600

x

y1tan

1800 -α

1800 +α 3600 –α or -α

α

O=?

2

300

Ex1.O=?, H=?

400

3

A

O

O=?, A=?

Θ=?

2

1

θ=?, O=?

• 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

r=?, θ=?

3-2 Adding and Subtracting Vectors

• Adding vectors Graphically

BAC

Connect vector head and tail, the sum vector is free tail to point free head

A

BC

BACD

A

B

CD

• Adding Vectors: parallelogram method

• Adding Vectors Using Component Cx=Ax+Bx

Cy=Ay+By

Ex1.

A=3, 200 ; B=5, 450 C=?

A

B

C

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

C

300

600

2

3

600

1600

200

A

B

• Subtracting Vectors

)( BABAD

Dx=Ax-Bx

Dy=Ax-By

Ex4.A= 10 m, 300; B=5 m, 600

Find , magnitude and direction ?

BAD