The document provides an overview of measurement principles in physics, discussing the definitions of standard measurement systems, including the metric and English systems, and concepts such as fundamental and derived quantities. It also explains the importance of uncertainty and error analysis in measurements, distinguishing between accuracy and precision, as well as random and systematic errors. Additionally, it covers statistical measures like variance and standard deviation for analyzing measurement data.

1. General Physics
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The
Measuring
Process

3. Measurement
Is the process of comparing
something with a standard.
To carry out measurements,
a system of standards and a
system of units should be
defined.

4. Two system of units have evolved;
• The Metric system
• The English system
The Metric System has two variations;
• The mks system
• the cgs system
The English system is otherwise known as
the;
• fps system

5. The fps system considers pound-
force as a fundamental quantity.
The counterpart of pound-force in
the metric system is mass.
The International System of Units,
abbreviated SI from the French
Le Système International d'Unitès,
is the modern form of the metric

6. It is the system of units that
the General Conference on
Weighs and Measures has
agreed upon and is legally
enforced in almost all parts
of the world.

7. Physical quantities may either be
fundamental or derived.
Fundamental quantities are basic
quantities which are independent
of one another.
(Length, mass, time,
thermodynamic temperature,
electric current, luminous intensity,
and amount of substance)

8. Derived quantities are
combinations of fundamental
quantities. Speed may be
defined as distance traveled
divided by time.
(Acceleration, density, work,
and energy)

9. The SI fundamental units are:
meter, kilogram, second,
kelvin, ampere, candela, and
mole.
The units for derived
quantities are combination
of these fundamentals units.

12. Nonstandard Units of Measurement
Dimension Unit of
Measurement
Description
Length Tinuro Length of a forefinger
Dali Breadth of a finger
Dangkal or dama
Width of a palm
Dipa Distance between the tip of the middle
finger of two extended arms
Length of a foot
talampakan
A single stride
Hakbang
Weight Dakot A handful
Kaing A container
Salop A conatiner
Kaban A container

13. Nonstandard Units of Measurement
Dimension Unit of Measurement Description
Volume Gusi A jar
Salok A scoop

15. Scientific
Notation and
Unit
Conversion

16. Scientific notation is a
convenient and widely used
method of expressing large and
small numbers. Any quantity may
be expressed in the form of Nx,
where N is any number between 1
and 10 and n is the appropriate
power of 10.

17. 1. The speed of light is approximately
300 000 000 m/s.
2. The mass of a strand of hair is
approximately 0.000 000 62 kg.
3. Express a.) 0.000 646 and
b.) 5 430 000 in Scientific notation

18. In expressing SI
measurements in scientific
notation, the SI prefixes
are used to denote
multiples and
submultiples of the SI
units.

19. SI
Prefix
Symbol Multiplier SI
Prefix
Symbol Multiplier
yotta- Y yocto- y
zeta- Z zepto- z
exa- E alto- a
peta- P femto- f
tera- T pico- p
giga- G nano- n
mega- M micro- m
kilo- k milli- µ
hecto- h centi- c

20. Quiz
1.Convert 55 km to
meters
2.Convert 12 g to
kilograms

21. Uncertainty
and Error
Analysis

22. Measurement always
have some degree of
uncertainty due to
unavoidable errors. Error is
the deviation of a measured
value from the expected or
true value. Uncertainty is a
way of expressing the error.

23. Accuracy versus Precision
Accuracy refers to the closeness of
a measured value to the expected or
true value of a physical quantity. On
the other hand, precision represents
how close or consistent the independent
measurement of the same quantity are
to one another.

24. Random versus Systematic
Errors
Random errors, as the name
suggests, result from unpredictable or
inevitable changes during data
measurement. Examples of causes of
random errors are electronic noise from
an electrical device, slight variation of
temperature when the volume of a gas is
being measured,

25. and uncontrollable presence of
wind when determining the period
of a simple pendulum. Random
errors affect the precision of
measurements. These errors may
be reduced by increasing the
number of trials of a measurement
and averaging out of the results.

26. Systematic Errors, on
the other hand, usually
come from the measuring
instruments or in the design
of the experiment itself.
These errors limit the
accuracy of one’s results.

27. Percent Error versus
Percent Difference
When there is an
expected or true value of
a quantity, percentage
error is usually calculated.

28. Percent error= x100%

29. Where - is the true or
accepted value
x- is the measured value
Percent error is usually
considered in judging the
accuracy of a measurement.

30. Percent difference is
a measure of how far
apart the different
measured values are from
each other, and is
therefore an indication of
precision.

31. Percent difference=

32. Where and are
two measured
values in an
experiment.

33. Problem 1.
Two trials were performed in
an experiment to determine the
latent heat of vaporization () of
water at 100. The values of of
water obtained were 532 cal/g and
536 cal/g. Find the percent
difference between the two.

34. Referring to Problem 1,
find the percent error for
each measurement if the
accepted value of of
water at 100 is 540 cal/g.

35. Variance
Another way to estimate errors
from multiple measurements of a
physical quantity is to determine the
variance of the set of measurements.
The variance measures the squared
deviation of each number in the set
from the mean.

36. The variance of a set
measurement is calculated step-
by-step as follows:
1. Take the mean of the set of
measurements, =
2.Take the deviation of each
measurement from the mean
(x-).

37. 3. Square each deviation, (x-)
4. Get the sum of the squares of
each deviation, ∑(x-)
5. Divide the sum of the squares by
the number of measurements in
the set,
In symbols, variance (=)

38. A variance of zero means
that all measurements are
identical. A small
variance indicates that the
values are close to one
another, which means they
are precise.

39. The square root of the variance
is the standard deviation. It is a
measure of how diverse or spread
out are a set of measurements
from their average. A small
standard deviation means that
most of the measurements are close
to their average.

40. A large standard deviation means
that the measurements are very
diverse. The measurement x of a
physical quantity in a set of
measurements is usually reported as
x= ± ó
Where is the mean of the set of
measurements and ó is the standard
deviation of the measurement.

41. During an experiment in a physics
laboratory class, a group of five
students was asked to measure the
period of a simple pendulum. Their
measurement were as follows: 2.3 s, 2.4
s, 2.2 s, 2.5 s, and 2.1 s. Determine the
a. mean, b. variance, c. standard
deviation, and d. measured period of
the pendulum.

42. In an experiment, 10 trials were
done to determine the range of a
projectile. The measurements for the
range of the projectile in centimeters
are as follows:
134.8 133.9 135.1 134.7 135.3
134.9 135.2 134.8 135.5 135.4

43. Absolute and Relative Uncertainties
A measurement must be
represented by two components:
1. a numerical or measured value
with the proper unit that gives the
best estimate of the quantity
measured and,

44. 2. The degree of uncertainties
in the measurement.
Uncertainty indicates the
range of values within which
the measurement is asserted to
lie with some level of
confidence.

45. The degree of
uncertainty may be reported
as absolute or relative.
Absolute uncertainty has
the same unit as the quantity
itself.

46. Relative uncertainty or
percent uncertainty, on the
other hand, is dimensionless
and is obtained by dividing the
absolute uncertainty by the
numerical or measured value.

47. Least Count
Absolute uncertainty is
usually based on the least
count of the measuring device.
Least count is the smallest
value that can be read from
any measuring device.

48. Graphical Analysis
Experiments in physics usually
involve changing a variable and
observing how another variable is
affected by this change. The
variable that is changed by an
experiment is called independent
variable.

49. The variable that is
affected by the change of
the independent variable is
called dependent
variable.