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1. PHYSICS AND
MEASUREMENT
•Standards of Length, Mass and Time
•Modelling and Alternative Representations
•Dimensional Analysis
•Conversion of Units
•Estimates and Order-of-Magnitude Calculations
•Significant Figures

2. The laws of physics are expressed as mathematical relationship
among physical quantities. In mechanics, the three fundamental
quantities are length, mass and time. All other quantities in
mechanics can be expressed in terms of these three.

3. WHY DO WE HAVE STANDARDS OF
LENGTH MASS AND TIME?

4. STANDARD OF LENGTH, MASS AND
TIME
Length –distance between two points in space
Mass –a measure of the amount of matter in an object
Time -isthe continued sequence of existence and events that occurs in
an apparently irreversible succession from the past, through the present,
and into the future

7. Thinker Bell
What do we do when we deal
with phenomenon that we can't
see with our naked eye?

8. Modelling and Alternative
Representations
If physicists cannot interact with some phenomenon directly,
they often imagine a model for physical system that is related to the
phenomenon.

10. Dimensional Analysis
In physics, the word “dimension” denotes the physical nature of a
quantity. The symbols we use to specify the dimensions of length, mass,
and time are L, M, and T respectively. Use bracket [] to denote the
dimension of physical quantity.
Eg; If we get the dimension of velocity then we let
[v]= speed
L = length ??????=
�
??????
T = time

12. Thinker Bell
Where do we apply dimensional
analysis?

13. In many situations, you may have to check as specific equation
to see if it matches your expectation. A useful procedure for doing
that, called dimensional analysis, can be used because dimensions
can be treated as algebraic quantities.
For example, quantities can be added or subtracted only if
they have the same dimension.
Furthermore, the terms on both sides of an equation must
have the same dimensions.

14. By following these simple rules, you can use dimensional analysis to
determine whether an expression has the correct form. Any
relationship can be correct only if the dimension on both sides of
the equation are the same.
Eg; Suppose you are interested in an equation for the position x of a
car at a time t if the car starts from rest at x=0 and moves with
constant acceleration a. Show that x=
1
2
��
2
is dimensionally
correct.

15. Show that the expression ??????=��,
where v represents speed, a
acceleration and t an instant of
time, is dimensionally correct

16. Seatwork1
Show the dimension of the
following is correct
Force, F=
��
??????
2
Pressure, P=
�
�??????
2

17. Suppose we are told that the acceleration a of a particle moving with
uniform speed v in a circle of radius r is proportional to some power of
r, say �
�
, and some power of v, say ??????
�
. Determine the values of n and
m and write the simplest form of an equation for the acceleration.

18. Conversion of Units
ENGLISH SYSTEM
eg, lb, ft, yard, in, oz …
SI UNITS
eg, kg, g m, mm, cm, N …

19. Thinker Bell
Why do we have to know how to
convert units?

20. When performing calculations with numerical values, it is
important to include the units so that we can detect errors if the units
for the answer turn out to be incorrect.
Conversion factors between SI and U.S. customary units of lengths are
as follows:
1 mile = 1609m = 1.609km 1ft = 0.3048m = 30.48cm
1m = 39.37in = 3.281 ft 1in = 0.0254m = 2.54cm

21. On an interstate highway in a rural
region of Wyoming, a car is
traveling at a speed of 38.0m/s. Is
the driver exceeding the speed
limit of 75.0mi/h?

23. Estimates and Order-of-Magnitude
Calculations
An order of magnitude is an approximation of the logarithm of a value
relative to some contextually understood reference value, usually 10,
interpreted as the base of the logarithm and the representative of
values of magnitude one.
??????=��10
??????
Where
1
√10
≤&#3627408462;<√10or approximately 0.316≤&#3627408462;<3.16the b
represents the order of magnitude of the number

24. Sample
0.0086;??????=0.86&#3627408485;10
−2
&#3627408462;=0.86&#3627408463;=−2
0.0021;??????=2.1&#3627408485;10
−3
&#3627408462;=2.1&#3627408463;=−3
720;??????=.72&#3627408485;10
3
&#3627408462;=.72&#3627408463;=3

25. What is the order of magnitude of
the following numbers.
1.3500 4. 840
2.0.042 5. 9.2
3.25

26. SIGNIFICANT FIGURES
The number of significant figures in a measurement can be used
to express something about the uncertainty. The number of significant
figures is related to the number of numerical digits used to express the
measurement,

27. Rules for significant figures
1.All nonzero digits are significant.
2.All zeros that are found between nonzero digits are significant.
3.Leading zeros (to the left of the first nonzero digit) are not significant.
4.Trailing zeros for a whole number that ends with a decimal point are
significant.
5.Trailing zeros to the right of the decimal place are significant.
6.Exact numbers, and irrationally defined numbers likeEuler’s number(e)
andpi(π), have aninfinitenumber of significant figures.
7.For any value written in scientific notation asA×10
x
, the number of significant
figures is determined by applying the above rules only to the value ofA; thexis
considered an exact number and thus has an infinite number of significant
figures.

28. In determining significant figure, zeros may or may not be significant figures.
eg,
0.03 0.030 1.03 1.030 300 300.0
0.0075 0.007501.0075 1.007507500 7500.0

29. USING SCIENTIIC NOTATION TO INDICATE THE NUMBER OF
SIGNIFICANT FIGURES
eg,
1. Express 1500 into a scientific notation
1.5&#3627408485;10
3
2 significant figures
2. Expand 2.3&#3627408485;10
−4
0.00023
3. Expand 2.30&#3627408485;10
−4
0.000230

30. Rewrite the following scientific
notations and identify how many
significant figures
1200
100100
505050
Rewrite the following into 4 significant
figures, 5 significant figures
4.05&#3627408485;10
−4
14&#3627408485;10
−4

31. When multiplying several quantities, the number of significant
figures in the final answer is the same as the number of significant
figures in the quantity having the smallest number of significant
figures. The same rule applies to division.
eg, ??????=??????&#3627408479;
2
where r=6.0cm
??????=??????6.0
2
??????=113.097355
??????=1.1&#3627408485;10
2
&#3627408464;??????
2

32. When numbers are added or subtracted, the number of decimal places
in the result should equal the smallest number of decimal places of
any term in the sum of difference.
eg, Consider the sum of 23.2 and 5.174
23.2 + 5.174 = 28.374
23.2 + 5.174 = 28.4

33. The rule for addition and subtraction can often result in answers that
have a different number of significant figures than the quantities with
which you start. For example, consider these operations that satisfy the
rule:
1.0001 + 0.003 = 1.0004
1.002 –0.998 = 0.004

34. A carpet is to be installed in a
rectangular room whose length is
measured to be 12.71 m and
whose width is measured to be
3.46 m. Find the area of the room.

35. SEATWORK2
1.Two spheres are cut from a certain
uniform rock. One has radius 4.50
cm. The mass of the other is five
times greater. Find its radius.
2.which of the following equations
are dimensionally correct?
(a) ??????&#3627408467;=????????????+&#3627408462;&#3627408485;
(b) &#3627408486;=(2??????)cos(??????&#3627408485;),
where k=2??????
−1
3. Kinetic energy K (Chapter 7) has
dimensions ??????&#3627408468;−??????
2
/ &#3627408480;
2
. It can be
written in terms of the momentum p
and mass m as ??????=
??????
2
2&#3627408474;
(a)Determine the proper units for
momentum using dimensional
analysis.
(b)The unit of force is the newton
N, where 1 N = 1 kg-m/s2 . What
are the units of momentum p in
terms of a newton and another
fundamental SI unit?