C02 - Scalar and Vector Quantities

Scalar and Vector Quantities
Prepared by: Ron Eric B. Legaspi

Most of the physical quantities encountered in physics are either
scalar or vector quantities.
Scalar quantity – is defined as a quantity that has magnitude only.
Examples: distance, ; time, ; speed, ; temperature, ; volume, ;

density, ; mass, ; and energy, .
Most of the physical quantities encountered in physics are either
scalar or vector quantities.
Vector quantity – is defined as a quantity that has both magnitude

and direction.
Examples: displacement, , , ; velocity, ; acceleration, ; force,

; momentum, ; and impulse, ⃗.
A vector is represented by an arrow.
Tail – represents the starting position

Tip/Arrowhead – represents the final position / Direction of
magnitude
Length – represents the magnitude (scaled)
Letter – represents the quantity
Examples of notations.
A. 50 km, 40° N of W
B. 30 km, 45° S of W
C. 40 km, 300° (std. pos.) 30°
D. 20 km, 30° course 40°

300° 55°
45°
50°
E. 60 km, 50° from –x axis
F. 50 km, -55° (std. pos.)
Graph the ff. vectors and indicate the scale used.
L. 20 km, 40° N of E
M. 65 mi, 120° from –x axis
N. 525 newtons, W
O. 300 m, 35° course
P. 65 yd, –120° from –y axis
Distance, – is a scalar quantity that refers to "how much ground an
object has covered" during its motion.
Displacement, – is a vector quantity that refers to "how far out of

place an object is"; it is the object's overall change in position.
When two or more vectors are added they yield the sum or resultant
vector. A resultant vector is the result or sum of vector
addition.
Vector addition is somewhat different from addition of pure numbers

unless the addition takes place along a straight line.
0 1 2 3 4 5 6 7 8
When two or more vectors are added they yield the sum or resultant
vector. A resultant vector is the result or sum of vector
addition.
Vector addition is somewhat different from addition of pure numbers

unless the addition takes place along a straight line.
0 1 2 3 4 5 6 7 8
Example 1:
A physics teacher walks 4 meters East, 2 meters South, 4 meters
West, and finally 2 meters North. Find the distance traveled by the
teacher and his displacement.
Example 2:
Use the diagram to determine the resulting displacement and the
distance traveled by the skier during these three minutes.
Example 3:
What is the coach's resulting displacement and distance of travel?
Graphical Method
- Parallelogram Method
- Polygon Method
Consider next the addition of vector quantities which are not in a
straight line.
For example, a person travels 4.0 miles, 40° north of east, and 3.0
miles, north. What is the resultant displacement?
y-axis
= 4.0 miles, 40° north of east

= 3.0 miles, north
= 6.4 miles, 61° N of E
x-axis
Example 4: Parallelogram
What is the resultant displacement if a man traveled 16 yd, 45° N of
E, and 10 yd, 35° E of S?
Example 5: Polygon (Tail-to-tip)

What is the total distance traveled and the resultant displacement if a
person moved 7 units north, 4 units east and another 3 units north?
= ?? N, ??° ? of ?
= 16 N, 60° N of E
= 8.0 N, 45° W of N
= 15 N, 60° W of S
= 20 N, 80° S of E
WORKING WITH SIGNS
Example 7: Parallelogram
Find the resultant force:
= 45 N, 180°
= –75 N, 330°
Note: Angular direction is in standard position, unless specified.

Analytical Method
- Pythagorean and Trigonometric Functions
- Sine and Cosine Law
- Component Method
Consider next the addition of vector quantities which are not in a
straight line.
For example, a person travels 4 miles east, and then 3 miles north.
What is the resultant displacement?
Using your knowledge in TRIGONOMETRY, find the angular
direction of the resultant.
Example 8:
What is the total distance traveled and the resultant displacement if a
person moved 7 units north, 4 units east and another 3 units north?
Example 9:
What is the resultant displacement if a man traveled 16 yd, 45° N of
E, and 10 yd, 35° E of S?
Example 10:
Find the resultant displacement of a boat that traveled on a course of
500 m north, 300 m at 20° north of east and 450 m north.
Example 11:
Give the resultant of the applied forces of 3.0 N, 60° west of south,
2.5 N west, 5.5 N north and 3.0 N, 10° east of north.
Components of a vector are vectors, which when added, yield the
vector.
F
Fy
Fx
Components of a vector are vectors, which when added, yield the
vector.
Example 12:
Find the x and y components of a 13 mile displacement at 22.6°
north of east.
Example 13:
Use the component method to find the resultant of a 5.0 N, 210° and
a 14 N at 120° forces.
Example 11:
Give the resultant of the applied forces of 3.0 N, 60° west of south,
2.5 N west, 5.5 N north and 3.0 N, 10° east of north.
Example 12:
Find the resultant displacement
and its angular direction by any
method.
R = ?? N, ??° ? of ?
B = 16 N, 60° N of E
D = 8.0 N, 45° W of N
C = 15 N, 60° W of S
A = 20 N, 80° S of E

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Scalar and Vector Quantities

Prepared by: Ron Eric B. Legaspi

Scalar quantity – is defined as a quantity that has magnitude only.

Examples: distance, ; time, ; speed, ; temperature, ; volume, ;

Vector quantity – is defined as a quantity that has both magnitude

Examples: displacement, , , ; velocity, ; acceleration, ; force,

Tail – represents the starting position

D. 20 km, 30° course 40°

Displacement, – is a vector quantity that refers to "how far out of

Vector addition is somewhat different from addition of pure numbers

Vector addition is somewhat different from addition of pure numbers

= 4.0 miles, 40° north of east

= 6.4 miles, 61° N of E

Example 5: Polygon (Tail-to-tip)

Note: Angular direction is in standard position, unless specified.

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