Unit 1 of Physics in the Leveling course at Yachay Tech University (Urcuquí, Ecuador). Semester October 2014-March 2015

1. UNIT 1: Description of the
physical world
Nivelación. Física

2. 1.1 Fundamental and derived physical
quantities
• Physics (knowledge of nature in Greek) is the
natural science that involves the study of
matter and its motion through space and
time, along with related concepts such as
energy and force.

3. 1.1 Fundamental and derived physical
quantities
• Physics is closely related to the scientific
method:
– Formulation of a question after an observation
– Hypothesis based on previous data and new ideas
– Predictions obtained with the hypothesis
– Testing the hypothesis by experiments
– Analysis in order to validate or deny the
hypothesis

4. 1.1 Fundamental and derived physical
quantities
• Physics not only tends to define phenomena
but also to measure them.
• Measurements need a standard, a basic unity.
• According to the International System there
are seven fundamental units, independent
between them.

5. 1.1 Fundamental and derived physical
quantities
• Longitude: meter (m)
• Time: second (s)
• Mass: kilogram (kg)
• Temperature: kelvin (K)
• Electrical current: ampere (A)
• Quantity of substance: mol (mol)
• Luminous intensity: candela (cd)

6. 1.1 Fundamental and derived physical
quantities
• However, there are a lot of units in Physics in
order to measure forces, electrical charges,
powers…
• These units will be a combination of
fundamental units.

7. 1.2 Measurement units
• Quantities must be accompanied by units.
• Figures and units are separated by a blank
space. They must be written correctly.
• The unit name depends on the language but
the first letter always is written in lower case.
• Very high and very low quantities can be easily
operated with multiples or submultiples
(power of 10).

8. 1.2 Measurement units

9. 1.2 Measurement units
• Scientific notation is very useful in Physics in
order to use very high or very low quantities.
• A∙10B, with A a real number between 0 and 1
and B an integer number, positive or negative
(or zero).

10. 1.3 Dimensional homogeneity of
equations
• Dimensional analysis is a quick method to
verify calculations.
• The addition or subtraction must be done with
the same dimensions.
• However, constants do not have dimensions,
so the exact result is not possible using
dimensional analysis.

11. 1.3 Dimensional homogeneity of
equations

12. 1.4 Results, errors and significant
figures
• Results must be written properly and with its
unit.
• But Nature is mischievous! The exact result is
never known. Errors are included by the
theory itself, the precision of the
measurement system and the numerical
operation.

13. 1.4 Results, errors and significant
figures
• X±DX is a typical expression in Physics
including the result and the positive and
negative errors.
• Significant figure is that its value is well-
known, not beyond the error.
• A in A∙10B is composed by significant figures. B
is the order of magnitude.
• Zeros used in order to place the decimal dot
are not significant figures.

14. 1.5 Scalar and vector quantities
• A scalar is a 1-D physical quantity described by
a single number. Scalars are the same for all
the different observers, i.e. they are not
dependent on the changes of reference
system.
• A vector is a 2-D magnitude represented in
the plane or in the space. It has modulus and
direction from the origin toward the point of
interest.

15. 1.5 Scalar and vector quantities
• A vector is represented
by an arrow.
• Vector components are
referred according a
coordinate system.
• Cartesian system has
three linear axes
perpendicular between
themselves.

16. 1.6 Vector operations
• Equality:
• Inversion:

17. 1.6 Vector operations
• Sum:
• Subtraction:

18. 1.6 Vector operations
• Vector multiplied by a scalar:
• Vector projected in an axis:

19. 1.7 Vector, scalar and triple products
• Vector product: c = a × b
– Two vectors (a, b) give another vector (c),
perpendicular to a and b.

20. 1.7 Vector, scalar and triple products
• Scalar product: c = a ∙ b
– Two vectors (a, b) give a scalar (c).

21. 1.7 Vector, scalar and triple products
• Triple product: d = c ∙ (a × b)
– Three vectors (a, b, c) give a scalar (d).
– The value d is the volume of the space generated
by these three vectors.