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Basic Physics
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Introduction
1. What is Physics?
2. Give a few relations between physics
and daily living experience
3. eview of !easure!ent and units "I#
$%&I'# %(G)I"*
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Scalar is a /uantity which only signifies its!agnitude without its direction. 0 4
%x. 15g of apple# 263 degreescentigrade# etc.
Vector is a /uantity with !agnitude and
direction. 0 4%x. +elocity of a !oving ob7ect 8 a carwith a velocity of 199 5!hr due to (orth
West# etc.
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Writing conformity
F Bold fontF Italic font signifying its magnitude
: (or!al :ont with an arrowhead on top of it (Use this)
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efining a +ector by;
1. 'artesian +ector
Ex. F = 59i + 59j + 29k N
the magnitude i F = !592
+ 592
+ 292
" F = ##.$$ N
%ue to &hich i the 'ector ((
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X (i)
Z(k)
Y(j)
F =
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efining a +ector by;2. >nit +ector
Ex. F = F u !ue the )re'iou exam)le"
=
F for magnitude !F2 = Fx2 + Fy
2 + F*2"
u for direction !dimenionle and unity"
u::
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agnitude F = !592 + 592 + 292"
F = ##.$$ N
%irection =
9.@6i 9.@67 9.335
α cos1 9.@6 A6.= 9 0angle fro! xaxis4
β cos1 9.@6 A6.= 9 0angle fro! yaxis4
γ cos1 9.33 69.6 9 0angle fro! Baxis4
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D 0i 4
E 0k 4
F 0 j 4
F CC.33 (
U
FU 9.@6i 9.@67 9.335
α
γ
β
α A6.= 9
β A6.= 9
γ 69.6 9O
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efining a +ector by;
3. Position +ector
"i!ilar to unit vector# it differs on how tolocate the vectors direction which isusing the point coordinate.
%x. : = : u !ee next exam)le"
r 0position vector4r 0position vector !agnitude4
u
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U
@ !
A ! 2
!
Given;
F 1
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"olution;
r r
u
: = : u
2i A7 @5
6.AC
9.26i 9.
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,perations of +ector
1. -ddition
2. "ubtraction3. ot Product
A. 'ross Product
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1. -ddition
:1
:2
= :1 :2
= 0:1x :2x4 i 0:1y :2y4 j 0:1B:2B4 k
θ
θ =y
x
&an 1
,
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1. -ddition
:1
:2
= :1 :2
= 0:1x :2x4 i 0:1y :2y4 j 0:1B:2B4 k
θ
θ =y
x
&an 1
,
esultant is directed
fro! initial tail towards
final arrow head
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2. "ubtraction
:1
:2
= :1 :2
= 0:1x :2x4 i 0:1y :2y4 j 0:1B :2B4 k
θ
θ = y
x
&an 1
,
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2. "ubtraction
:1
:2
= :1 :2
= 0:1x :2x4 i 0:1y :2y4 j 0:1B :2B4 k
θθ =
y
x
&an 1,
&a5e note and watch
out HHH
0the sense is
opposite to the givendiagra!4
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3. ot Product
:
d
θ
D 0i 4
E 0k 4
F 0 j 4
:
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- . B - cos θ 0General :or!ula4 { {
Vector Magnitude
{
The angle between
vectors (between their
tails)
'artesian >nit vector dot )roduct
i . i =
i . j = / i . k = / k . j = /
j . j = k . k =
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:ro! %xa!ple;
J F . d :d cos θ 0>sing +ectors !agnitude4
0:xi :y 7 :B54 . 0dxi dy 7 dB54
:x dx :y dy :B dB 0>sing 'o!ponent +ector4
&he dot product of two vectors is called scalar product
since the result is a scalar and not a vector
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0he dot )roduct is used to deter !ine;
1. &he angle between the tails of the vectors.
+%'&, -( "'-)-
θ cos1
- . B
-
2. &he pro7ected co!ponent of a vector 1 onto an axis
defined by its unit vector u
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W e l c
o m e t o t h e
J u n g l e
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D 0i 4
E 0k 4
F 0 j 4
B
-
3
: 199
(
θ
Given ; :igure 1
e/uired;
1. θ
2. :- 0$agnitude4
:ig.1
%xa!ple;
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"olution ;
1. Angle θ
:ind position vectors fro! to - and to 'r - 299i 8 2997 1995
r ' 9i 8 3997 1995 8 3997 1995
cos θ r - . r 'r - r '
9 @9999 19999
69999
=AC@= 9.63C
θ 'os 1 9.63C A2.A< o 0answer4
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"olution ;
r -u-
r -
2. F BA
299i 8 2997 1995
399 9.@@6i 8 9.@@67 9.335
r 'u'
r '
9i 8 3997 1995
[email protected] 8 9.=A=7 9.31@5
:' :' . u' 199 . 08 9.=A=7 9.31@54 =A.=7 31.@5
:- :' . u- 0=A.=i 31.@74 . 09.@@6i 8 9.@@67 9.3354
@3.3 19.< 63.C ( 0answer4
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"olution ;
Alternative Solution
:- 0199 (4 0cos A2.A<o4
63.6= (
:- :- u- 63.6= 09.@@6i 9.@@67 9.3354
A=.2i 8 A=.27 2A.3
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A. 'ross Product
B
-
F
D 0i 4
E 0k 4
F 0 j 4
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- x ' A is eual to B cross !
-pply the right hand rule
i
j k
i x 7 5
7 x 5 i
5 x i 7
7 x i 5
5 x 7 i
i x 5 7
i x i 9
7 x 7 9
5 x 5 9
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Right Hand Rule
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Right Hand Rule
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Right Hand Rule
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Right Hand Rule
44. (answer for
yourself)
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- x '
0x i y j B k 4 x 0'x i 'y j 'B k 4
i j k
x y B
'x 'y 'B
0y 'B 8 B 'y4i 0B 'y 8 x 'B4 j 0x 'y 8 y 'x4" -
i j k
x y B
'x 'y 'B
i j
x y
'x 'y
0y 'B 8 B 'y4i 8 0x 'B 8 B 'x4 j 0x 'y 8 y 'x4"
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- x '
0x i y j B k 4 x 0'x i 'y j 'B k 4
i j k
x y B
'x 'y 'B
0y 'B 8 B 'y4i 0B 'y 8 x 'B4 j 0x 'y 8 y 'x4" -
i j k
x y B
'x 'y 'B
i j
x y
'x 'y
0y 'B 8 B 'y4i 8 0x 'B 8 B 'x4 j 0x 'y 8 y 'x4"
Full cautionfor the +6 ign
and
u,cri)t
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%xa!ple; Given ; :igure 2
e/uired ;
1. $o 0$o!ent at
point ,4
2. $y 0$o!ent
about y axis4
B
-
F = //N
D 0i 4
E 0k 4
F 0 j 4
o
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"olution;:inding the vectors needed
: : u
199A99i 8 2
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B
-
F = // N
D 0i 4
E 0k 4
F 0 j 4
o
7// j
7//i + 5/j 8 2//k
F = #./i 8 7#.9j 8 $9./7k
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$o
$o 1
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$o
$o 1