1. Introduction and Mathematical Concepts
Chapter 1
Introduction and Mathematical Concepts

2. Physics has developed out of the efforts
1.1 The Nature of Physics
Physics has developed out of the efforts
of men and women to explain our physical
environment.
Physics encompasses a remarkable
variety of phenomena:
planetary orbits
radio and TV waves
magnetism
lasers
many more!

3. Physics experiments involve the measurement
1.2 Units
Physics experiments involve the measurement
of a variety of quantities.
These measurements should be accurate and
reproducible.
The first step in ensuring accuracy and
reproducibility is defining the units in which
the measurements are made.

4. SI units meter (m): unit of length kilogram (kg): unit of mass
second (s): unit of time

5. 1.2 Units

6. The units for length, mass, and time (as
well as a few others), are regarded as
base SI units.
These units are used in combination to
define additional units for other important
physical quantities such as force and
energy.

7. A scalar quantity is one that can be described by a single number:
1.5 Scalars and Vectors
A scalar quantity is one that can be described
by a single number:
temperature, speed, mass
A vector quantity deals inherently with both
magnitude and direction:
velocity, force, displacement

8. 1.6 Vector Addition and Subtraction
Often it is necessary to add one vector to another.

9. 1.6 Vector Addition and Subtraction

10. 1.6 Vector Addition and Subtraction
When a vector is multiplied
by -1, the magnitude of the
vector remains the same, but
the direction of the vector is
reversed.

11. 1.7 The Components of a Vector

12. 1.7 The Components of a Vector

13. 1.7 The Components of a Vector
It is often easier to work with the scalar components
rather than the vector components.

14. 1.8 Addition of Vectors by Means of Components

15. 1.8 Addition of Vectors by Means of Components

16. Example 1.1
A vector A has a magnitude of 20cm at 200⁰, and a vector B has a magnitude of 37cm at 45⁰. What is the magnitude and direction of vector difference A – B?
Solution:
Vector
Distance
Angle
X-component
Y-component A
20cm
200⁰
Ax = 20cos200⁰
Ay = 20sin200⁰ B
37cm
45⁰
Bx = 37cos45⁰
By = 37sin45⁰
A – B
-44.95cm
-33.00cm

17. Magnitude: |A - B|= [(Ax – Bx)2 + (Ay – By)2]
= [(-44.95)2 + (-33.00)2]2
= 55.76cm
Direction: θ = tan-1 [(Ay – By)]/[(Ax – Bx)]
= [-33.00/-44.95]
= 36.28⁰
= ⁰

18. Problems to be solved
1.36, 1.51, 1.52, 1.57, 1.63, 1.65
B1.1: A disoriented physics professor drives 4.92km east, then 3.95km south, then 1.80km west. Find the magnitude and direction of the resultant displacement, using the method of components.

19. B1.2: The three finalists in a contest are brought to the centre of a large, flat field. Each is given a meter stick, a compass, a calculator, a shovel, and (in a different order for each) the following three displacements: 72.4m, 32⁰ east of north, 57.3m, 36⁰ south of west, 17.8m straight south. The three displacements lead to the point where the keys to a new Porsche are buried. Two contestants start measuring immediately, but the winner first calculates where to go. What does he calculate?

20. B1. 3: After an airplane takes off, it travels 10. 4km west, 8
B1.3: After an airplane takes off, it travels 10.4km west, 8.7km north, and 2.1km up. How far is it from the take-off point?