Differences between Scalars and Vectors

Contributed by:

Jonathan James Thu, Jan 20, 2022 05:45 PM UTC

The highlights are:
1. Vector addition
2. Non-Collinear Vectors
3. Vector and Polar coordinates

1. Vectors and Scalars
Eng. Ahmed
Eng. Abdulslam

2. Scalar and Vectors
 A SCALAR is any  A VECTOR is any
quantity in physics quantity in physics
that has that has BOTH
MAGNITUDE, but MAGNITUDE and
NOT a direction DIRECTION.
associated with it.
 Such as { speed }  Such as {Acceleration }

3. Applications of Vectors
VECTOR ADDITION – If 2 similar vectors point in the SAME
direction, add them.
VECTOR SUBTRACTION - If 2 vectors are going in opposite
directions, subtract them.

4. Applications of Vectors
 Example: A man walks 54.5 meters east, then 30
meters west. Calculate his displacement relative to
where he started?
54.5 m, E
-
30 m, W
24.5 m, E

5. Applications of Vectors
 Problem:
Car moves 80 Km east, then 30 Km west. After that it
moves again 50 Km east .
Calculate its displacement relative to where it started?
100 Km , East

6. Non-Collinear Vectors
When 2 vectors are perpendicular, you must use the Pythagorean theorem.
Key of chapter

7. The direction?
We follow these graphs :
N
W of N E of N
# North
N of E
# South N of W
# East W E
S of W S of E
# West
W of S E of S
S

8. Non-Collinear Vectors
Example: A boat moves with a velocity of 15 m/s, N in a river
which flows with a velocity of 8.0 m/s, west. Calculate the
boat's resultant velocity with respect to due north.
2 2
8.0 m/s, W Rv  8  15 17 m / s
15 m/s, N
8
Rv  Tan   0.5333
15
 Tan  1 (0.5333) 28.1
The Final Answer : 17 m/s, @ 28.1 degrees West of North

9. Non-Collinear Vectors
Example : A plane moves with a velocity of 63.5 m/s at 32
degrees South of East. Calculate the plane's horizontal and
vertical velocity components.
x
32
y
63.5 m/s
X = 53.85 m/s , east .
Y= 33.64 m/s , south .

10. Non-Collinear Vectors
 Problem :
R = 14.3 Km
Angle : 65° N of E

11. Vectors and Polar
Coordinates

12. Four Quadrants
 
 R   R
Ry   Ry
Rx Rx
 
Rx   Rx
  
 
Ry Ry
R R
Problem
Problem :: suppose
suppose :: 
=
=40
40
o
o what
what are
arethe
the


13.  Problem :
X = 86.60 m
Y= - 50 m

14. Thank You

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