phisics lecture note 3

8/12/2019 phisics lecture note 3

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PHYSICS CHAPTER 1

1

Scalar quantity is defined as a quantity with magnitude only.

e.g. mass, time, temperature, pressure, electric current, work,

energy and etc.

Mathematics operational : ordinary algebra

Vector quantity is defined as a quantity with both magnitude &direction.

e.g. displacement, velocity, acceleration, force, momentum,

electric field, magnetic field and etc.

Mathematics operational : vector algebra

1.2 Scalars and Vectors



PHYSICS CHAPTER 1

2

Table 1.6 shows written form (notation) of vectors.

Notation of magnitude of vectors.

1.2.1 Vectors

Vector ALength of an arrow – magnitude of vector A

displacement velocity acceleration

s

v

a

s av

vv

aa

s (bold) v (bold) a (bold)

Direction of arrow – direction of vector A

Table 1.6



PHYSICS CHAPTER 1

3

Two vectors equal if both magnitude and direction are the same.

(shown in figure 1.1)

If vector A is multiplied by a scalar quantity k

Then, vector A is

if k = +ve, the vector is in the same direction as vector A.

if k = - ve, the vector is in the opposite direction of vector A.

P

Q

Q P

Figure 1.1

Ak

Ak

A

A



PHYSICS CHAPTER 1

4

Can be represented by using:

a) Direction of compass, i.e east, west, north, south, north-east,

north-west, south-east and south-west

b) Angle with a reference line

e.g. A man throws a stone with a velocity of 10 m s-1, 30 above

horizontal.

1.2.2 Direction of Vectors

30 v

x

y

0



PHYSICS CHAPTER 1

5

c) Cartesian coordinates

2-Dimension (2-D)

m)4m,2(),( y x s

s

y/m

x/m

4

20



PHYSICS CHAPTER 1

6

3-Dimension (3-D)

s

2

3

4

m2)3,4,(),,( z y x s

y/m

x/m

z /m

0



PHYSICS CHAPTER 1

7

d) Polar coordinates

e) Denotes with + or – signs.

N,12050 F

F

120

+

+-

-



PHYSICS CHAPTER 1

8

There are two methods involved in addition of vectors graphically i.e.

Parallelogram

Triangle

For example :

1.2.3 Addition of Vectors

Parallelogram Triangle

B

A

B

A

B A

O

B A

B

A

B A

O



PHYSICS CHAPTER 1

9

Triangle of vectors method:

a) Use a suitable scale to draw vector A.

b) From the head of vector A draw a line to represent the vector B.

c) Complete the triangle. Draw a line from the tail of vector A to the

head of vector B to represent the vector A + B.

A B B A

Commutative Rule

B

A

A B

O



PHYSICS CHAPTER 1

10

If there are more than 2 vectors therefore

Use vector polygon and associative rule. E.g. RQ P

RQ

P

R

Q

P

Q P

RQ P RQ P

Associative Rule

RQ P



PHYSICS CHAPTER 1

11

Distributive Rule :

a.

b.

For example :

Proof of case a: let = 2

B A B A

A A A

number realare,

B A B A

2

B

A

B A

O B A

2



PHYSICS CHAPTER 1

12

A

2O

B

2

B A

22

B A B A

222

B A B A

22



PHYSICS CHAPTER 1

13

Proof of case b: let = 2 and = 1

A

A A A

312

A

3

A A A A

12

A

2 A

A

3

A A A

1212



PHYSICS CHAPTER 1

14

For example :

1.2.4 Subtraction of Vectors

Parallelogram Triangle

D

C

O

DC

O

D

DC DC

C

D

DC

C

D

DC



PHYSICS CHAPTER 1

15

Vectors subtraction can be used

to determine the velocity of one object relative to another object

i.e. to determine the relative velocity. to determine the change in velocity of a moving object.

1. Vector A has a magnitude of 8.00 units and 45 above the positive x

axis. Vector B also has a magnitude of 8.00 units and is directed alongthe negative x axis. Using graphical methods and suitable scale to

determine

a) b)

c) d)(Hint : use 1 cm = 2.00 units)

Exercise 1.2 :

B A

B A

B2 A

B A2

phisics lecture note 3

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