Transcript Outline

Chapter 1: INTRODUCTION
• Physics: branch of physical science that deals
with energy, matter, space and time.
• Developed from effort to explain the behavior
of the physical environment.
• Summary: laws of Physics, Formula, graphs.
• Basis of rocket/space travel, modern
electronics, lasers, medical science etc.
• Major goal: reasoning critically (as a
physicist), sound conclusions, applying the
principles learnt.
• We will use carefully defined words, e.g.
velocity, speed, acceleration, work, etc.
§ 1.3: The Use of Mathematics
• Factor (or ratio) – number by which a
quantity is multiplied or divided when
changed from one value to another.
• Eg. The volume of a cylinder of radius r and
height h is V = r2h. If r is tripled, by what
factor will V change?
• Vold = r2h, Vnew = (3r)2h = 9. r2h, Vnew/Vold
= 9. V will increase by a factor of 9.
(a) Decreasing the number 120 by 30% gives ---(b)Increasing the number 120 by 30% gives -----
Proportion
• If two quantities change by the
same factor, they are directly
proportional to each other.
• A  B – means if A is doubled, B
will also double.
• S  r2 – means if S is decreased by
factor 1/3, r2 (not r!) will also
decrease by the same factor.
Inverse Proportion
• If A is inversely proportional to B – means
if A is increased by a certain factor, B will
also decrease by the same factor.
• K inversely proportional to r [K 1/r] –
means if r is increased by factor 3, K will
decrease by the same factor.
• The area of a circle is A = r2.
(a)If r is doubled, by what factor will A
change?
(b)If A is doubled, by what factor will r
change?
§ 1.4: Scientific notation:
• Rewriting a number as a product of a number
between 1 and 10 and a whole number power
of ten.
• Helps eliminate using too many zeros.
• Helps to correctly locate the decimal place
when reporting a quantity.
• Eg: Radius of earth = 6,380,000 m
= 6.38 x 106 m
Radius of a hydrogen atom
= 0.000 000 000 053 m = 5.3 x 10-11 m.
Precision/Accuracy in Scientific
Measurements
• In reporting a scientific
measurement, it is important to
indicate the degree of precision and
the accuracy of your measurement.
• This can be done using absolute (or
percentage) error, significant figures
and order of magnitude, etc.
(a)Absolute/Percentage error:
Eg. Length of a notebook = 27.9 ± 0.2 cm
 Actual length is somewhere between 27.9
– 0.2 and 27.9+0.2, ie 27.7 and 28.1 cm
 ± 0.2 is the estimated uncertainty (error).
 0.2 is the absolute uncertainty (error).
 27.9 is the central value
 27.7 and 28.1 are called extreme values.
Percentage Uncertainty
Absolute Error
x 100
Percentage uncertainty =
Central Value
Eg. Length of a notebook = 27.9 ± 0.2 cm
% Uncertainty = 0.2
x 100  0.7%
27.9
AbsoluteError
Fractional Error 
CentralValue
0 .2

27.9
Examples
• The length of a table was found to
be 1.5 m with 8% error. What was
the absolute error (uncertainty) of
this measurement?
• The mass of a bag was found to be
12.5 0.6 kg. What was the percent
error in this measurement?
Error Propagation in Addition/Subtraction
The absolute error in the sum or difference of
two or more numbers is the SUM of the
absolute errors of the numbers.
x  x and y  y
Sum  ( x  y )  (x  y )
Difference  ( x  y )  (x  y )
Eg. 8.5  0.2 cm and 6.9  0.3 cm
Sum = 15.4  0.5 cm
Difference = 1.6  0.5 cm
Error Propagation in Multiplication/Division
The fractional error in the product or quotient of
two numbers is the SUM of the fractional errors of
the numbers.
x  x  x and y  y  y
x
y
Fractional errors : in x is
and in yis
x
y
Pr oduct  P  L1.L2
P
x y
Fractional error in P is
which is (  )
P
x
y
L1
Quotient  Q 
L2
Q
x y
Fractional error Q is
which is (  )
Q
x
y
Error Propagation in Multiplication/Division
Eg. x = 8.5  0.2 cm and y = 6.9  0.3 cm
Fractional errors:
0 .3
0
.
2
in y =
=
in x =
=
6 .9
8 .5
Find the product, P = x.y and its
absolute uncertainty (P).
Examples
The area of a circle is A = r2.
(a)If r is doubled, by what factor will A
change?
(b)If A is doubled, by what factor will r
change?
(b) Significant Figures:
Number of reliably known digits in a
measurement. Includes one “doubtful” or
estimated digit written as last digit.
Eg. 2586
[6 is the last digit. It is the doubtful digit].
Eg. 25.68
[8 is the last digit. It is the doubtful digit].
Significant Figures contd:
• All nonzero digits are significant.
• Zeros in between significant figures are
significant.[2,508]
• Ending zeros written to the right of the decimal point
are significant. [0.047100]
• Zeros written immediately on either sides of decimal
point for identifying place value are not significant.
[0.0258, 0.258]
• Zeros written as final digits are ambiguous.[25800] To
remove ambiguity, rewrite using scientific notation.
• Eg. (i) 58.63 – 4 sf, (ii) 0.0623 – 3 sf, (iii) 5.690 x 105 – 4
sf. (iv) 25800 – 2.58x 104 = 3 sf, 2.580x 104 = 4 sf,
2.5800x 104 = 5 sf.
Significant Figures in Addition/Subtraction
The sum/difference can not be more precise
than the least precise quantities involved.
ie, the sum/difference can have only as many
decimal places as the quantity with the least
number of decimal places.
Eg: 1) 50.2861 m + 1832.5 m + 0.893 m =
2) 77.8 kg – 39.45 kg =
“keep the least number of decimal places”
Significant Figures in Multiplication/Division
The product/quotient can have only as many
sf as the number with the least amount of sf.
Eg: 1) What is the product of 50.2861 m
and 1832.5 m?
2) What is 568 m divided by 2.5 s?
“keep the least number of significant figures”
(c) Order of Magnitude
– (roughly what power of ten?) To determine
the order of magnitude of a number:
• Write the number purely as a power of ten.
• Numbers < 5 are rounded to 100
• Numbers  5 are rounded to101
• Eg. 754 =7.54 x 102 ~101 x 102 = 103. The
order of magnitude of 754 is 3.
• 403,179 = 4.03179 x 105 ~100 x 105 = 105 =
5 O/M
• 0.00587 ~ orders of magnitude = - 2 (how?).
What is the difference between
accuracy and precision?
Precision:
• Reproducibility or uniformity of a result.
• Indication of quality of method by which a set of
results is obtained.
• A more precise instrument is the one which gives
very nearly the same result each time it is used.
• A precise data may be inaccurate!!
Accuracy:
• How close the result is to the accepted value.
• Indication of quality of the result.
• A more accurate instrument is the one which gives a
measurement closer to the accepted value.
Precise/Accurate
Precise/Not Accurate
Not Precise/Accurate
Not Precise/Not Accurate
§ 1.5: Units
We will use the SI system of units
which is an international system of
units adapted in 1960 by the General
Council of Weights and Measures.
• In SI system:
Length is measured in meters (m).
Mass is measured in kilograms (kg).
Time is measured in seconds (s).
• Other fundamental quantities and
their units in the SI system includes
Temperature (in Kelvin, K),
Electric current (in Amperes, A)
Amount of substance (in mole, mol) and
Luminosity (in Candela, cd).
• The SI system is part of the metric
system which is based on the power of
ten.
Converting Between Units
Eg. Convert 65 miles/hour to SI units.
1 mile = 1.609 km = 1609 m.
1 hour = 3,600 seconds
65 miles 65 x 1609m

 29.1 m / s
1 hour
1 x 3600s
§ 1.6: Dimensional Analysis
Dimensions – Units of basic
(Fundamental) quantities:
Mass [M], Length [L], Time [T]
We can only add, subtract or equate
quantities with the same dimensions.
Eg. 1 Check if the expression v = d2/t is correct,
where v = speed (in m/s), d is the distance (in
m) and t is time (in s).
Quantity Dimension
[ L]
V
[T ]
d2
T
v = d2/t
[L]2
[T]
[ L] [ L]2

[T ] [T ]
Hence eqn is
not correct
Eg. 2: If the equation was now
correctly written as v = kd2/t, what
must be the units of k?
2
[ L]
[ L]
1
k
k
[T ]
[T ]
[ L]
The units of k must be m-1
§ 1.7-1.9: Reading Assignment