units, measurements, dimensional analysis

1. Measurement and unit
Physical quantity
 Its any quantity that can be measured e.g length
Unit
 A physical quantity is expressed as a number with units e.g length:
L=2m, time; t=1s.

2. S.I Units
• S.I stands for systeme internationale in French, meaning
“international system”.
• SI units are agreed international standard units.
• Base quantities are measured in SI units

3. • Basic physical quantities are quantities which are not expressed in
terms of other quantities.
• They are also called fundamental physical quantities.
• The SI units of base quantities are called basic units or fundamental
units.

4. Table 1: Base Physical Quantities
Quantity SI Unit Name Unit Symbol
Mass kilogram kg
Length meter m
Time second s
Electric current Ampere A
Temperature Kelvin K
Amount of substance mole mol
Luminous intensity candela cd

5. Derived quantities
• are expressed in terms of basic quantities by multiplication or
division.
• Table 2 shows some examples of derived quantities.

6. Table 2: Derived Quantities
Derived Quantity Unit Name Unit Symbol
Force Newton N
Acceleration Meter per second square
Pressure Pascal Pa
Work Joule J
Power Watt W (J/s)
Density Mass per volume Kg/m³
2
/ s
m

7. Unit Prefixes
• For larger and smaller units, we write them in a short hand by
multiply by powers of 10 as in Figure 3.
•Alternative writing method
•Using standard form
•N × 10n where 1  N < 10 and n is an integer

8. Table 3:Unit Prefixes
Prefix Symbol Factor Prefix Symbol Factor
Peta P deci d
Tera T centi c
Giga G milli m
Mega M micro µ
Kilo k nano n
Hector h pico p
Deca da fento f
15
10
12
10
9
10
6
10
3
10
2
10
10
1
10
2
10
3
10
6
10
9
10
12
10
15
10

9. Changing units
• Replace the unit you are given with the equivalent quantity in the unit
you want
• Example : Write 72km/hr in m/s
 
s
m
s
m
hr
km
therefore
s
s
X
hr
m
km
/
20
3600
72000
/
72
,
3600
60
60
1
72000
72






10. OTHER UNIT SYSTEM
i. U.S. customary system: foot, slug, second
ii. Cgs system: cm, gram, second
iii. British Engineering system: (the gravitational version)
foot, slug, seconds

11. CONVERSION OF UNITS
• We will use SI units in this course, but it is useful to know
conversions between systems.
• 1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm
• 1 m = 39.37 in. = 3.281 ft 1 in. = 0.0254 m = 2.54 cm
• 1 lb = 0.465 kg 1 oz = 28.35 g 1 slug = 14.59kg
• 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds
• More can be found in Appendices A & D in your textbook.

12. EXAMPLE
On an interstate highway in a rural region of Wyoming, a car is traveling at a
speed of 38.0 m/s. Is the driver exceeding the speed limit of 75.0 mi/h?
SOLUTION
COMMENT; The driver is indeed exceeding the speed limit and should slow
down.

13. DIMENSIONS
• The word dimension has a special meaning in physics. It denotes the
physical nature of a quantity.
• Whether a distance is measured in units of feet or meters or
fathoms, it is still a distance. Its dimension is length
• Each base quantity is considered a dimension denoted by a specific
symbol written within square brackets

14. DIMENSIONS, UNITS AND EQUATIONS
Quantities have dimensions:
Length – L, Mass – M, and Time - T
Quantities have units: Length – m, Mass – kg, Time – s
To refer to the dimension of a quantity, use square brackets, e.g. [F]
means dimensions of force.

15. Dimensional Analysis
• Dimensional analysis can assist in the checking a specific equation to
see if it matches your expectations.
• Because dimensions can be treated as algebraic quantities.
For example,
i. quantities can be added or subtracted only if they have the same
dimensions.
ii. The terms on both sides of an equation must have the same
dimensions.

16. EXAMPLE
Use dimensional analysis to check the validity of the following
expressions.
i.
SOLUTION
Note: For the equation to be dimensionally correct, the quantity on
the right side must also have the dimension of length. i.e.
in any equation, the LHS and RHS must have the same
dimensions.
ANALYSIS OF EQUATION

17. ii.
• Each term must have same dimension
• Two variables can not be added if dimensions are
different
• Multiplying variables is always fine
• Numbers (e.g. 1/2 or p) are dimensionless

19. ANALYSIS OF POWER LAW
Example:
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 r n, and
some power of v, say v m. Determine the values of n
and m and write the simplest form of an equation for
the acceleration

20. We write the relation as
:a ∝ rn
vm
a = krn
vm
where k isthe proportionality constant
Writing the equation dimensionally, we get
LT−2
= k[L]n
[LT−1
]m
k isdimensionless, so we can take it out of the equation
LT−2
= [L]n
LT−1 m
LT−2
= Ln
Lm
T−m

21. equating the powers, we get
1 = n + m and − 2 = −m
from which, we get m = 2 and n = −1
Therefore, the derived equation is
a = k
v2
r

22. END OF PRESENTATION