physics vector by : vidyamandir classes

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Chapter - 1

Course for IITJEE - 2012

PHYSICSPHYSICSIntroduction to VectorsIntroduction to Vectors



Y 5 a _

b _

6

–X +X

c _

4

–Y

d _

7

a _

a _

a _

a _

-a _



a _

2a _

– 3a _

j

i

O

Y

–X X

–Y –2i

3i

1.5j

– 4j



a _

5b _

4

a + b _

_

| a + b| = | a | + | b | = 9 units _

_

_

_

3

a _

8

b _

a + b _

_

5

| a + b| = | a | – | b | if | a | > | b | _

_

_ _

_

_

| a + b| = | | – | |b a if | b | > | a | _

_ _

_

_

_

a +

b_

_

a _

b _

a + b_

_

b _

a _

O

Q _

P _

q

Q

q R

a

PO



c

a

b

a b

c

3 R

5

60 a



Y

X

i

a_

j

O

Y

X

j

i

P Aax

a _

ay

B

q

O

a = s in qy a

a cos q= ax



2

c _

1b_

2

3

a _

1

1

Y

OX

5

60° 60°

5 sin 60°

5 cos 60°

645°

6 sin 45°

6 cos 45° 45°

30°

10

10 sin 30°

10 cos 30°30°



10

30°

60°

8

10 sin 30°

8 cos 60° 10 cos 30°

8 sin 60°

Ry

Rx

Rq



2 120°

2

2 cos 30°

2 sin 30° 2

Ö3R

q

1



a 30°

b

10

a cos 30°

a sin 30°

10

b

q

a

60°

5

5

5 sin 60°

a cos q 5

5 cos 60°

a sin q



F

120°

120° 120°F

F

X

Resolving F cos 60°

F cos 60°

F sin 60°

F

F sin 60°

F2

135°

90°F1

10Ö2 N

F2

F1

45° 1 0 Ö 2 c s 4 5 o °

1 0 Ö s i 4 5

2 n °

Y

X



A

W1 20 N

B

50 NW2

T (tension in string B)B

W = 50N (wt. of block)2

TA

TB W1

W1



B

60°

O

W

A

100 N

60°

T0

100 N

ÞT = 100 N0

T cos 60°2

T sin 60°2

T0

T1

B

A



N1

B

15 N (wt. of B)

N1

A

20 N (wt. of A)N2

s t r i n g

q

P l a n eq

q

normal

N

m g s i n q

T

mg cos qq

mg



A

B

30°

C

NA

T 1

W s i n

q A

q

WA

W cos qA

W i n

q s

B

W

c o s q

B

WB

q

T 2

T 1

N B

T2

WC

F1

30° A B F = 15 N2



NB

F = 15 N2RB

20 N (wt. of B)

NA

AR

30 N

30°

F1



f

0.1 N

mNs

N

25 N

100 N

W sin 30°

N

W30°

W cos 30°

mNs

30°

F



F sin 30°

mNs F cos 30°

W

N

30°

n 3 W s i 0 °

N1 T

m N 1 k

W cos 30°

W

N2

mNk 2

W

T



T

W

37°

R

mR

B A

37°

W

R 1

RmR1

mR

T1

T2

B

C

A

O

T2 T1

C B

10Ö3 10 N

T = 10Ö32 T = 10 N1

T1

q

q

T2

O

T (tension in0

string OA)



T1

T0

T2

Y X

q

T3T1

T2

W2 W1

53° 37°

T2

T3

W2

53°

53°

T2

T1

W1

37°

37°



T1

O

T3

T2

60°

T2

T1

60°

T3

30°

T

W

T = 10

30°

T1

T2

T2

W



q

w

w

q

T T

W

qq

W

T

T = W

2 0 0 N

w

37°

A 45°

W

N

100

f T1

T cos45°0

T2

N

T sin45°0T0

T1

T2

W

45°



F = 50 N40

R

50N

40N

mR

45°

F

70g

N



a + b_

_

a

_

b _

a + b_

_

b _

a _

O

Q

q R

a

PO



· Chapter Tests–80 tests fortesting concepts learned ineach chapter.

· Unit Tests–20 unit tests to

check the ability to combineconcepts from chapters in thatunit.

· Test Series–20 test seriesfor testing cumulativelearning.

· Revision Tests – ability to goback to any of the tests andtest yourself again afterrevising concepts to measureimprovement.

Online Tests

· Detailed Solutions– you getto see solutions explaining indetail the approach andtechniques used.

· Reporting and Analysis–Over 11 distinct reports whichshow test based results as wellas cumulative reports thatshow performance over time.

· Comparison Testing– thereporting contains a measureof your performance ascompared to others.

Analysis and Reporting· Access to forums forproblem solving anddiscussions.

· Forums are moderatedby teachers and IITiansto provide the highestlevel of responses.

Online Forums

· Detailed and highlyorganized studymaterial.

· 80 chapters full of solved examples andillustrations to supportthe theoreticalconcepts.

Course Material

Study Test

AnalyzeDiscuss

Student

Correspondence Course - How it works

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