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Basic DynamicsVector Analysis
Vector and Scalar Quantities
Vector that has both
is a
physical quantity magnitude and direction
scalar has but direction
quantity only magnitude no
> distance speed , ,
mass , temperature , volume , density
>
displacement velocity weight
, , ,
force , acceleration and momentum .
Addition of vectors
when two vectors act in the same direction , the resultant vector is their addition .
1- ,
resultant force
D
F- Fit 72
-
Dots
5ubtractionofuectors.tl
If the need to take and the other
vectors act in opposite directions , we one direction as positive as
negative .
☐F '
q, resultant force
f , f, + C- Fa) = Fi -
f-2-
SOH
aµÉ
opp CAH TOA
J /
R Ft
sino-opp-coso-adj-tano-opp.gg
,
=
adj ' "
YP
tan '( %) ☒ hyp hyp adj
-
/ R ② =
,
Resolving Perpendicular Vectors : when two vectors are
acting on each other at 90° The
.
resultant
vector is the of the F
diagonal rectangle .
Fy - - -
t - -
-
lengthy magnitude of (F) JÉi=
¥
É
I
Direction of (F) =Q tan
"
( %✗) I
§ Vy
=
v
Cfx ) and G- y)
, yy
E
Magnitude
:
of components are ,
Fx =FcosQ and 9- ✗ = Fsi no ÉÉÉ Fu
horizontal component
, Resolving vectors
acting
at
angles
f-2 72
0-1<90%0-1 0--2>90402 obtuse
angle)
acute
angle )
__
-_
2
10-1 F ,
Fi
9- is obtained
by resolving horizontal and vertical components .
In Class Questions
-
p
)
velocity Cms
"
vectors and scalars both have magnitude , direction :
right or left ,
magnitude speed
: .
a vector has both magnitude and
direction but a scalar has
only magnitude .
0 ( magnitude and direction)
Fa 9- cos 300=86-6
-
- ( 873in Calculate the distance and magnified
9- y= F-since = 1008in 300=5 ON
Distance -2001-1501-2001-205
800M
7=-5+5
=
Magnitude ? ? =
1501-250
F=JÉo '
why ? /
=
400m
F- I calculate:
a) Distance
9- = 30N i -
b) Displacement
Distance -5km 1- 2km -_ 7km
c)
Displacement -I=a7b?2abcos(
a) Displacement from into 5km ÉÉÉs)
b 2km 745° = 6.57km ( 7km)
3km
←A
N
Total distance = 3km 1- 4km = 7km
w o magnitude .tn#y b) Calculate magnitude
=FÉ & =
c) direction
5km (displacement from 0)
*
b) magnitude -_F=Ñt
=
s
F== 104.4N
100mA
c) tan
- '
(0%0)
b) Calculate magnitude and direction
7 A =
'
3°
zom , ,
Fy
Ñ+
magnitude > F-
122.98 -123N
" On
Direction tan "(¥s )
magnitude __JÉ=
-
113.1N ✗
63-40 (8%0)--450
DFN
7 = '
Direction tan
-
=
ggn at 90°
> Forces
are so
ÉtÉÑ
F- F , =ÑÉ = 1. I ✗ 105N ,
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