This document provides an overview of key concepts in physics, including: - Physics is the science that describes the basic components of the universe and forces. It underpins other sciences. - Physical quantities have numerical values and units, and can be basic or derived. Basic quantities include length, mass, and time. - Vectors have magnitude and direction, while scalars only have magnitude. Examples of each are provided. - Methods for adding and subtracting vectors graphically and by components are described. Properties of vector operations are also summarized.

1. LO 1.1: USE PHYSICAL QUANTITIES
A PowerPoint Presentation by
Projecte H. Assistant Lecturer of
Physics
IPRC Kigali
Academic year 2022-2023

2. • What is Physics?
• The Scientific Method.
• How Should I Study Physics?
Photo: Courtesy of NASA
Testing the Mars Rover

3. What is Physics?
Physics is the science of nature which
describes the basic components of the
universe, the forces and their effects.
Physics is the most basic of
the sciences, underpinning all
other disciplines of science,
medicine, and engineering.
Physicists are problem solvers,
often meeting new challenges
and developing new theories.
NASA

4. Where might I work as
a physicist?
A strong physics background
prepares you for almost any
occupation that involves science
or engineering.
NIST
High
Voltage
NASA
Mars Rover

5. The main objective of physics
Is to help people to understand the origin
of natural phenomena. Through
1. Observation: Consists of examining
attentively and in detail all stages of
the phenomenon
2. Experimentation: Consists of
reproducing a phenomenon to derive
its general laws.

6. Physical Quantities and measurements
 In the quest to understand nature,
scientists use physical quantities to
describe the world around us.

7. 1.PHYSICAL QUANTITIES
 A physical quantity is a quantity that can be
measured.
A physical quantity have numerical value
and unit of measurement.
●For example temperature of 30 degrees
celcius, 30 is numerical value & ‘degree
celcius’ is the unit. Written as 30o C.
*
Temperature = 30 degree Celcius = 30o c
Physical quantity = numerical value x unit measurement

8. ●Basic Quantities
are physical quantities that cannot be
derived from other physical quantities.
In physics we have 7 basic quantities

9. • Derived Quantities are physical quantities
derived from combination of basic quantities
through multiplication or division or both
Derived Quantities Symbol Relationship with basic quantities Derived units
Area A Length x Length m2
Volume V Length x Length x Length m3
Density ρ Mass
Length x Length x Length
kg/m3
Velocity v Displacement
Time
m/s
Acceleration a Velocity
Time
m/s2
Force F Mass x Acceleration N
Work W Force x Displacement J
Energy Ep
Ek
Mass x gravity x high @
½ x mass x velocity x velocity
J
Power P Force x Displacement
Time
W
Pressure p Force
Area
N/m 2
some of the derived quantities and their respective derived unit

10. measurement of physical
quantity
To measure a physical quantity is to compare it with other
quantity of comparable nature taken as unit.
No measurement is ever perfectly accurate. Even with
high precision instruments, some error is inevitable.
An error is the difference between the measured value and
the actual value.
There are 2 main types of errors in measurement
Systematic errors and Random errors
Systematic errors are due to the error in calibration of
instruments
Eg: Zero error is due to non-zero reading when the actual
reading should be zero

11. Random errors
Are Due to mistakes made by observer when taking
measurement either through incorrect positioning of the eye
(parallax) or the instruments when taking measurement
 It may also occur when there is a sudden change of
environmental factors like temperature, air circulation and
lighting

12. PREFIXES
● Prefixes are used to simplify the description
of physical quantities that are either very big
or very small.
Prefix Symb
ol
Value
tera T 1012
giga G 109
mega M 106
kilo k 103
hecto h 102
deka da 10
desi d 10-1
centi c 10-2
mili m 10-3
micro H 10-6
nano n 10-9
pico P 10-12
some commonly used SI prefixes

13. Scalar quantities and vector quantities
Scalar quantities (or sometimes known as
scalars) are those quantities which are
characterized by magnitude only .
Example of scalar quantities: mass,
density, volume, pressure, work, etc.
2. Vector quantities
1.Scalar quantities
Vector quantities are those quantities which
are characterized by magnitude and
direction.

14. *
Example of vector quantities: Force, displacement, acceleration,
velocity, etc.
1. Point of application (origin)
2. Direction (line of action of a vector)
3. Orientation
4. Magnitude
 Graphical representation and properties of vectors
1. Graphical representation of Vectors
A vector is schematically represented as an oriented segment
of a straight line from point A, called the origin (or the
tail) of the vector, to point B, called the end (or the head)
of the vector.
Characteristics of a vector

15.  The length of a vector is called its magnitude.
 The magnitude of vector is denoted by but
sometimes the magnitude of is denoted by AB.
Types of vectors
 Collinear vectors: are vectors which have common line
of action.
 Equal vectors: The vectors, which are parallel to each
other and have the same direction (i.e. same sense) and
equal in magnitude are known as equal vectors.
 Opposite Vectors: The vectors having same
magnitude but opposite direction, are known as opposite
vectors.

16.  Unit vector: vector whose magnitude is unity i.e
magnitude is equal to1, is known as unit vector.
 Null Vector: The null vector is a vector whose
origin is at the same time as its end. The
magnitude of zero vector is zero. Its direction is not
defined.
 Coplanar Vectors: Vectors lying in the same
plane are called coplanar vectors.
 Co-initial Vectors (concurrent): Vectors are
said to be co-initial, if they have a common initial
point.

17. Properties of vectors
1. Addition of vectors by graphical method
 Given two vectors , their sum or their resultant
is the vector obtained by joining the tail of the first vector
to the head of the second vector when the head of the
first vector is coinciding with the tail of the second vector.
a) Triangle method of adding vectors
On vectors, one can perform operations of
addition, subtraction and multiplication.
Addition of vectors

18. •Parallelogram method of adding vectors
Polygon method of adding vectors

19. Subtraction of vectors
• Given a vector , we define the negative
of this vector to be a vector with the
same magnitude as but opposite in
direction.
Eg.

20. 2. Adding vectors by components
Consider first a vector that lies in a particular
plane. It can be expressed as the sum of two other
vectors, called the components of original vectors
x
y
x
y
V
V
V
V
V
V






tan
cos
sin
and

21. In space, a vector has three
components and
The sum of two vectors
• and

22. Properties of addition of vectors
1. The addition of vectors is
commutative:
2. The addition of vectors is
associative:
1. HANDOUTS
2. NOTES
3. PROBLEMS
4. EXAMS
5. LABS
6. RESOURCES
Hole
Punch

23. Multiplication of vectors
1. The scalar product of vectors
1. The scalar product of 2 vectors is commutative
2. For any vector , the following relation holds:
The scalar product (dot product) of two vectors ,
denoted by , is a scalar equal to the product of their
magnitudes A and B, multiplied by the cosine of the
angle between those vectors.
Properties of a scalar product

24. 3. Given 2 vectors ,
5. Scalar product is distributive relative to the addition.
For any vectors
Thus the equality to zero of the scalar product of two
non zero vectors expresses the condition of the
perpendicularity of two vectors
iff
4. The vectors of the orthonormal basis verify the following
relations:

25. 6. Given 2 vectors
Then,
This property allows us also to find the expression for
the cosine of the angle between vectors

26.  The direction of is perpendicular to the plane
formed by and is obtained using right hand rule
or Screw rule.
 The magnitude is the area of a parallelogram
constructed by using these two vectors:
The vector product of two vectors

27. Properties of the vector product
1. The vector product is anti-commutative:
2. The vector product is distributive relative to the addition of
vectors:
3. Given 2 vectors , if or at least one of vectors
is zero.
Thus the equality to zero of the vector product of two non zero
vectors expresses the condition of the parallelism of two
vectors. iff

28. 4. Let be unit vectors forming an orthonormal
basis, then
Given and , then
Salus Method

29. •
Law Method