1. Scalars and VectorsScalars and Vectors
By: Lee Yi LiangBy: Lee Yi Liang
Joshua Foo and Ryan WongJoshua Foo and Ryan Wong

2. What is scalar?
• Scalar quantities only takes into
account the magnitude of a
measurement, but not its direction.
This is where it differs from vector
quantities.

3. Examples of scalar
quantities
• Speed: 100km/h; Vector would be
velocity: 100km/h heading north
• Temperature: 30o
C
• Time: 10s

4. Vectors
• Quantities with magnitude and
direction
• Have positive and negative quantities

5. Vectors
• All vectors can be broken up into 4
parts
– North
– South
– East
– West
• Magnitudes of vectors can be compared
– |A| compared to |B|

6. Vectors
• Example:
– Displacement
– Velocity
– Acceleration
– Force
– Electric field

7. How to represent a vector?How to represent a vector?

8. How? Like This!
• Scaled vector diagrams
• Depict a vector by use of an arrow
drawn to scale in a specific direction

9. Huh but how?
• All vector diagrams should contain
the following:
– Clearly listed scale
– Vector arrow in specified direction
– Vector arrow must have
• a head
• a tail
– Cleary labeled magnitude and direction
of vector
– In this case, magnitude is 20m and
direction is 30 degrees west of north

10. • Ohh like that ar?

11. SOLVING RESULTANT OF 2
VECTORS
Geometrically

12. Things to note
• Dot represents the object
• Arrows represent the forces.
• Length of arrows represent
magnitude of forces.
• Direction arrows are pointing to
represent direction of forces.

13. Scenario
• Let’s say, there are two forces acting
on an object. One force is acting
100N upwards, the other is 50N to
the right.

14. Step 1 – Drawing object
and forces
.
100N
50N

15. Step 2 – Move one arrow
along the other
.
100N
50N
OR
.
100N
50N

16. Step 3 – Draw an arrow from
object to point where the moved
arrow is touching
.
100N
50N
OR
.
100N
50N

17. Step 4 – Measure length of
resultant arrow
• After you find out the length of the
arrow, find out the ratio of the
resultant arrow to the ratio of any of
the beginning arrows.
• Hence deduce the force.

18. How to determine theHow to determine the
resultant of 2 vectorsresultant of 2 vectors
mathematically?mathematically?

19. But then but then but
then hor
• In the diagram, R is the
resultant displacement of
displacement vectors A, B, and
C
• A + B + C = R
• In all such cases, the resultant
vector is the result of adding
the individual vectors

20. But then but then but then
still got more
• Pythagoras Theorem
– Can be used to determine the result of
adding two (and only two) vectors which
make a right angle to each other

21. But then never mind
• Trigonometry
– Can be used to determine direction of
resultant vector

22. Result of more vectors
• Forces in a Plane
• Forces in 90 degrees
• Forces in all directions

23. Result of more vectors
• Forces in Plane
– Simply add all the forces together

24. Result of more vectors
• Forces in 90 degrees
– Add up the vector forces in north and south
– Add up the vector forces in east and west
– Make a right angle triangle
– Use trigonometry to find resultant force

25. Result of more vectors
• Addition of Vector
– Represent the vector forces with
arrows
• Greater magnitude, longer arrow
– Place all the arrows at the same starting
point
– Choose an arrow
– Choose the next arrow
• At the end of the 1st
arrow, place the start
of the 2nd
arrow

26. Result of more vectors
– Continue until all the arrows are joint
together
– All the arrows should end at a point
• Match this ending point to the starting point
– This new arrow is the resultant force

27. Acknowledgements
• The Physics Classroom -
http://www.physicsclassroom.com/Class/vectors
The Electronic Science Tutor -
http://www.physchem.co.za/Vectors/index.htm
Resultant of Forces -
http://www.walter-fendt.de/ph11e/resultant.htm

28. The End
• Qs?