THEORIES AND PRINCIPLES OF PHYSICS  
The discipline of physics is built upon a foundation of theories and principles  
that have been developed and refined over centuries of scientific exploration.  
These theories and principles serve as the building blocks for understanding the  
laws and phenomena that govern the natural world.  
Therefore, in this section, we shall discuss the aspect of scientific investigation  
and the existing basic theories and principles of physics.  
Basic principles of scientific investigations  
The basic principles of scientific investigations form the foundation of the scientific  
method and guide researchers in conducting systematic and reliable experiments.  
These principles are essential for ensuring the accuracy, objectivity, and productibility  
of scientific findings.  
The concept of scientific investigation  
The scientific method is the basic skill needed in the world of science.  
Humans are always curious about why and how things happen in the world.  
The scientific method provides scientists with a well-structured platform to help  
find the answers to their questions.  
Therefore, the scientific method is a set of steps used by scientists to investigate  
a problem or answer questions.  
The following are steps followed when carrying out a scientific investigation.  
1. Problem identification  
This is the first step in the scientific method. It is when one makes a puzzling  
observation.  
An example of such an observation would be 'What is the relationship between the  
length of the string to which the pendulum bob is attached and the time taken by the  
pendulum to complete a given number of oscillations? The following examples will help  
you to build competence on how to identify a problem.  
Example 1.  
When a ball is released from the top of a ramp, it rolls down to the bottom. After  
several trials, you notice that the ball always stops at almost the same point. How  
can you identify the problem in this scenario?  
Answer: The problem in this scenario is to explain why the ball consistently stops  
at almost the same point on the ramp during each trial. This issue could be related  
to factors such as friction, air resistance, or the ramp's incline.  
Example 2  
A student conducts an experiment to measure the time taken for a pendulum to  
complete ten oscillations. However, the results are inconsistent as the measured  
time varies significantly between trials. What problem can be identified in this  
experiment?  
Answer: The problem in this experiment is to identify the factors causing the  
inconsistency in the time measurements for the ten oscillations of pendulum. Key  
issues in this scenario may be variations in the starting angle, air resistance, or  
inaccuracies in the timing method.  
2. Formulating a testable hypothesis  
A hypothesis is a scientific assumption or prediction of the outcome.  
It is a suggestion of the answer to the question asked.  
To formulate a testable hypothesis in physics, we must make observations on a  
variety of events. For example, the length of the string to which the pendulum  
bob is attached affects the time taken by a pendulum to complete a given number  
of oscillations.  
The following examples may help you to formulate a testable hypothesis.  
Example 1  
You notice that when you rub a balloon against your hair, it becomes negatively  
charged, and you can make small pieces of paper stick to it. What testable  
hypothesis can you formulate to explain this phenomenon?  
Answer: Hypothesis; If the balloon is rubbed against the hair, it will become  
charged and hence attract lightweight objects, like small pieces of paper, due to  
static electricity.  
Example 2  
During a solar eclipse, you observe that the temperature drops noticeably.  
Formulate a testable hypothesis to investigate this temperature change  
phenomenon.  
Answer: Hypothesis: If a solar eclipse occurs, then there will be a decrease in  
temperature compared to normal conditions, due to the obstruction of the sun's  
radiation towards the Earth's surface.  
TEST YOURSELF  
You notice that some metal objects left outside during a cold night feel much colder  
to the touch than other objects made of wood or plastic. Propose a testable  
hypothesis to explain this observation.  
Fact  
In science we never prove a hypothesis through a single experiment because there is a  
chance that you made an error somewhere along the way. What you can say is that,  
your results support or do not support the original hypothesis.  
3. Conducting an experiment  
Scientists particularly physicists experiment to study the causal relationships. This is  
done by manipulating one or more independent variables and measuring their effects  
on one or more dependent variables. There are three different types of variables,  
namely; dependent, independent, and controlled variables.  
(a) Dependent variable; A variable which changes if the experimental condition  
changes. For example, the dependent variable is the time it takes for the pendulum  
bob to complete a given number of oscillations.  
(b) Independent variable; A variable which does not change even when the  
experimental condition is changed. For example, the length of the pendulum bob  
is independent variable.  
(c) Controlled variable; This is a variable that is kept constant during an experiment.  
For example, the number of oscillations is a controlled variable.  
Designing Physics experiments  
Designing an experiment involves creating a set of procedures to systematically  
test a hypothesis. This requires a strong understanding of the system under  
study.  
For valid conclusions, the selection of a representative sample and controlling  
any extraneous variables is important.  
To experiment, we need first to understand how to identify the experimental  
variables. The following examples will help you to build skills on how to  
identify the variables that need to be manipulated.  
Example 1  
A student is investigating how the height of a ramp affects the distance a toy car travel.  
The student changes the height of the ramp and measures the distance the car travels  
as shown in Figure below. Identify the dependent, independent, and controlled  
variables in this experiment.  
ca  
Floor  
Answer  
(a) Dependent variable; The distance travelled by the toy car.  
(b) Independent variable; The height of the ramp.  
(c) Controlled variables; The type of toy car used, the starting point of the car on  
the ramp, and the surface of the ramp.  
4. Data collection and analysis  
Data collection involves recording what has been observed during the  
experiments.  
The observed results are tabulated (recorded in a table form) and ready for  
analysis. This involves plotting graphs and calculating mean, standard  
deviation, and errors. The results of the experiment can be recorded as shown in  
Table below.  
Table 1: Length of the string to which the pendulum bob is attached and time taken to  
complete number (n) of oscillations.  
T2 (s2)  
Length, L (m)  
(n) Period, T (s)  
Time  
to complete  
Number of  
observations  
oscillations, t (s)  
5. Data presentation and interpretation  
Data presentation involves the use of charts, graphs and mathematical formulae.  
Drawing graphs in Physics  
For all graphs plotted from experimental data, it is important to remember that  
you should not just connect the dots.  
Data do not always follow a line or curve perfectly.  
By obtaining several experimental data points any discrepancies in each data  
point can be removed.  
The data points plotted should be fitted by drawing the best line that describes  
the distribution of data points.  
The graphs you plot must have the following features:  
(a) The graph must have a clear descriptive title which outlines the relationship  
between dependent and independent variables with their appropriate units in  
brackets e,g A graph of temperature (oc) against time t (s).  
(b) An appropriate scale is used for each axis so that the plotted points must occupy  
enough axis/space (work out the range of the data and the highest and lowest  
points). The scale must remain the same along the entire axis and should use easy  
intervals such as 10 s, 20 s and 50 s. Use graph paper for accuracy.  
(c) Each axis must be labelled with what is shown on the axis and must include the  
appropriate units in brackets, e.g. Temperature (0C), time (s) and height (cm).  
(d) The independent variable is generally plotted along the x-axis, while the  
dependent variable is generally plotted along the y-axis. Each point has an x and  
y co-ordinate and should be plotted with a symbol which can be easily seen, e.g.,  
a cross or circle.  
(e) A best fit line should be drawn to the graph. Do not start the graph at the origin  
unless there is a data point for (0,0), or if the best fit line runs through the origin.  
(f) If there is more than one set of data drawn on a graph, a different symbol (and/or  
colour) must be used for each set and a key or legend must be included to define  
the symbols.  
(g) Use line graphs when the relationship between the dependent and independent  
variables is continuous. For a line graph, you can draw a line of best fit with a  
ruler. Make sure the number of points is distributed fairly and evenly on each side  
of the line. Example of a graph of square of the period, T 2 (s2) against length, L  
(m) is shown in Figure below.  
Figure: Graph of square of period, T2(s2) against length, L(m)  
(h) In an exponential graph, a best fit line should be drawn by using freehand.  
After recording and analysing the data, you may look for possible trends or patterns  
and explain why they occur that way. For instance, physicists may notice that as the  
length of the string to which the bob is attached increases, the time to complete a given  
number of oscillations also increases. This pattern forms the basis on which evidence  
can be obtained.  
6. Drawing a conclusion  
A conclusion is a summary of the result of the experiment.  
It includes a statement that either proves or disapproves of the hypothesis.  
SCIENTIFIC THEORY  
A theory in physics is a big idea or explanation that scientists come up with to  
describe how something in nature behaves.  
For example, the theory of gravity explains why things fall down when we drop  
them. It says that all objects with mass are attracted to each other, and that's why  
we stay on the ground and do not float on air. Many theories explain various  
physical phenomena. In this section, we shall concentrate on the theory of  
gravity and its impact human beings.  
Theory of gravity  
The theory of gravity is the fundamental theory that explains the force of attraction  
between two objects that have mass.  
▪ It says that objects with mass are attracted to each other.  
▪ The force of attraction between such objects is referred to as the force of gravity.  
This force is very important for our daily activities.  
▪ All objects on the earth are attracted toward the earth because the earth is more  
massive than other objects.  
Significance of the theory of gravity  
(i) It explains the arrangement and motion of planets, moon, and other celestial  
bodies in the solar system and beyond.  
(ii) Helps to understand the tides and Earth's motion around the sun.  
(iii) Provide the basis for space exploration and satellite technology.  
(iv) It influences our daily lives, from walking on the earth's surface to the launching  
of spacecraft into space.  
LAWS OF PHYSICS  
In physics, a law is a scientific statement that describes a physical phenomenon under  
certain conditions in nature.  
▪ Physical laws provide important insight into the nature of the universe, and they  
are developed from several observations in nature. However, physical laws do  
not explain the mechanism by which a phenomenon occurs.  
▪ Physical laws are applicable to all objects regardless of scenario but are only  
meaningful within certain contexts. Examples of physics laws are the Hooks  
law and the law of floatation.  
1. Hooke's law  
Hooke's law is a law of physics that explains the force needed to extend or compress  
a spring by distance x.  
Hooke’s law states that "provided the elastic limit is not exceeded, the extension is  
directly proportional to the force applied. "  
2. The law of floatation  
The law of flotation is a crucial principle for understanding why certain objects rise or  
submerge in fluids.  
It determines whether the object will float or sink based on its density relative to the  
surrounding medium.  
The law of floatation states that ‘‘a floating object displaces its own weight of fluid  
in which it floats’’  
PRINCIPLES OF PHYSICS  
In physics, a principle is a general rule or explanation of how a specific physical  
phenomenon occurs.  
▪ Essentially, a principle is a fundamental truth that forms a foundation for  
explaining a physical phenomenon in nature.  
▪ In addition, principles describe some specific fundamental concepts.  
Developing a principle requires more explanations than the requirement for a  
physical law. It is for this reason; that physicists need to follow the method of  
scientific investigation when developing a physical principle. Examples of  
physics principles are Pascal's principle, Archimede's principle and the  
principle of conservation of energy.  
1. Archimedes' principle  
Archimedes' principle is a fundamental concept in fluid mechanics, named after Greek  
mathematician and scientist Archimedes. The principle explains the buoyant force  
experienced by an object immersed in a fluid, such as water or air.  
The Archimede’s principle states that "Any object partially or totally immersed in a  
fluid experience an upthrust which is equal to the weight of the fluid displaced by  
the object".  
▪Archimedes' principle helps to understand why objects float or sink and has a  
practical application in various engineering and everyday scenarios.  
2. Pascal's principle  
Pascal's principle accounts for the transmission of pressure in fluid.  
Pascal's principle states that "When pressure is applied at any point on the  
surface of a fluid contained in a closed container, the pressure is transmitted  
undiminished to all parts of the fluid and to the walls of the container".  
3. The principle of conservation of energy  
The principle of conservation of energy emphasises that the total energy in a system is  
conserved.  
▪This principle allows us to analyse complex systems, predict their behaviour, and  
understand how energy flows and transforms, providing a fundamental  
framework for understanding the physical world. The principle of  
conservation of energy states that ‘‘Energy can neither be created nor  
destroyed but it can be transformed from one form to another’’