1.     Physical Quantities Quantities that can be measured
Careful observations
experiment  
precise 
Accurate measurement

2. Physical Quantities Quantities that can be measured
Examples:
Length
Mass
Time
Weight
Electric current
Force
Velocity
energy
Describing a physical quantity:
50 kg
unit
Numerical value

3. Different units can be used to describe the same quantity
Example :
The height of a person
can be expressed
in feet
In inches
In metres ……

4. unit
Is the standard use to compare different magnitudes of the same physical quantity

5. Thermodynamic temperature
standard
SI Units
Quantity
SI unit
Symbol
Length
metre m
Mass
kilogram kg
Time
second s
Electric current
Ampere A
Thermodynamic temperature
Kelvin K
Amount of substance
mole
mol
Light intensity
Candela cd
Base quantity

7. International Prototype Metre standard bar made of platinum-iridium
International Prototype Metre standard bar made of platinum-iridium. This was the standard until 1960
The metre is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom
In 1960

8. The metre is the length of the path travelled by light in vacuum during a time interval of 1⁄299 792 458 of a second.
In 1975
…………………

9. prefixes Prefix Factor Symbol pico 10-12 p nano 10-9 n micro 10-6 
Milli
10-3 m
centi
10-2 c
deci
10-1 d
kilo
103 k
Mega
106 M
Giga
109 G
Tera
1012 T
prefixes

10. Is a combination of different base quantities
Derived quantities
Is a combination of different base quantities
Derived unit = the unit for derived quantity
= is obtained by using the
relation between the derived
quantities and base quantities

11. Derived quantity
Derived unit
Area m2
Volume m3
Frequency Hz
Density
kg m-3
Velocity
m s-1
Acceleration
m s-2
Force
N or kg m s-2
Pressure Pa

12. Specific heat capacity
Derived quantity
Derived unit
Energy or Work
J or Nm
Power
W or J s-1
Electric charge
C or As
Electric potential
V or J C-1
Electric intensity
V m-1
Electric resistance
 Or V A-1
Capacitance
F or C V-1
Heat capacity
J K-1
Specific heat capacity
J kg-1 K-1

13. Dimensions of Physical quantities
Is the relation between the physical quantities and the base physical quantities
Example 1 :
Area
Dimension of area =
Length x Breadth =
L x L =
= L2
Unit of area = m2

14. Example 2 :
Velocity
Dimension of velocity =
Displacement
Time = L T =
= L T-1
Unit of velocity = m s-1

15. Example 3 :
Acceleration
Dimension of acceleration =
Change of velocity
Time =
L T-1 T =
= L T-2
Unit of acceleration = m s-2

16. Example 4 :
Force
Dimension of force =
Mass x Acceleration =
M x L T-2 =
= M L T-2
Unit of force = kg m s-2
or N

17. Example 5 :
Energy
Dimension of energy =
Force x Displacement =
M L T-2 x L =
= M L2 T-2
Unit of energy = kg m2 s-2
or J

18. OR
Example 5 :
Energy
Dimension of energy =
Mass x Velocity x Velocity =
M x L T-1 x L T-1 =
= M L2 T-2
Unit of energy = kg m2 s-2
or J

19. Example 6 :
Charge
Dimension of electric charge =
Current x Time =
A x T =
= A T
Unit of area = A s

20. Example 7 :
Frequency
Dimension of frequency =
1 .
Period = 1 T =
= T-1
Unit of frequency = s-1

21. Example 8 :
Strain
Dimension of strain =
Extension
Original length = L =
= 1
dimensionless
Unit of frequency = no unit

22. _ = + Uses of Dimensions Dimensional homogeneity of a physical
equation
Both have same dimensions _
1st
Physical
quantity
2nd
Physical
quantity = +

23. Every term has the same dimension
Case 1
Example :
v2 = u2 + 2as
Every term has the same dimension
L T
L2 T-2 v2 = =
L T
L2 T-2 u2 = =
L T-2 L
L2 T-2
2as = =
The equation is dimensionally consistent

24. The equation is incorrect.
Case 2
Example :
v = u + 2as
[v] =
[u] 
[2as]
L T-1
L T-1 v = =
L T-1
L T-1 u = =
L T-2 L
L2 T-2
2as = =
The equation is incorrect.
The dimension is not consistent

25. A physical equation whose dimensions are consistent need not necessary be correct :

26. dimensionally consistent
The constant of
proportionality is wrong
Case 3
Example :
v2 = u2 + as
Every term has the same dimension
L T
L2 T-2 v2 = =
L T
L2 T-2 u2 = =
L T-2 L
L2 T-2 as = =
The equation is incorrect.
The equation is
dimensionally consistent

27. dimensionally consistent
Has extra term
Case 4
Example : s2 t2
v2 = u2 + 2as +
L T
L2 T-2 v2 = =
Every term has the same dimension
L T
L2 T-2 u2 = =
L T-2 L
L2 T-2
2as = = L2 T2 s2 t2
L2 T-2 = =
The equation is incorrect.
The equation is
dimensionally consistent

28. The truth of a physical equation can be confirmed experimentally :

29. Example :
The period of vibration t of a tuning fork depends on the density , Young modulus E and length l of the tuning fork. Which of the following equation may be used to relate t with the quantities mentioned? A E l g
gl3  E AE  Al
a) t =
b) t =
c) t =
Where A is a dimensionless constant and g is the acceleration due to gravity. The table below shows the data obtained from various tuning forks made of steel and are geometrically identical.
Frequency/Hz
256
288
320
384
480
Length l /cm
12.0
10.6
9.6
8.0
6.4

30. Use the data above to confirm the choice of the right equation
Use the data above to confirm the choice of the right equation. Hence, determine the value of the constant A.
For steel: density  = 8500 kg m-3 ,
E = 2.0 x 1011 Nm-2

31. dimensionally consistent
Solution : A E
The equation is
dimensionally consistent l g
gl3  E AE 
b) t = Al
a) t =
c) t =
Unit for E =
N m-2
= ( ) m-2
kg m s-2
Mass
volume
[] =
= kg m-1 s-2
[E] =
M L-1 T-2
[t] = x x T +
M L-3
L-3 A E
(L T-2) L3 = L2
gl3
T-1 =
M L-1 T-2
L-1 T-2
= T

32. dimensionally consistent
Solution : A E l g
gl3  E AE  Al
a) t =
b) t =
c) t =
[t] = T
Mass
volume  E
M L-3 Al
[] = = L
M L-1 T-2
dimensionally consistent
The equation is
L-2 = L
T-2
L-1 = L
T-1
= T

33. l l Solution : The dimension is not consistent [t] = T Hence,A E l g
gl3  E AE  Al
a) t =
b) t =
c) t =
[t] = T
Hence,
the equation
is incorrect
M L-1 T-2 l g L AE  =
M L-3
L T-2 1 L2
T-2 =
T-1
= L2 T-1

34. l l Solution : Which one is the right equation? t against l t against
gl3  E AE  Al
a) t =
b) t =
c) t =
Which one is the right equation?
Frequency/Hz
256
288
320
384
480
Length l /cm
12.0
10.6
9.6
8.0
6.4
t against l 3 2
t against l
Plot a graph

35. 1 period = frequency Frequency /Hz 256 288 320 384 480 Length l /cm
12.0
10.6
9.6
8.0
6.4 1
256 1
288 1
320 1
384 1
480
period, t, s
3.91x10-3
3.47x10-3
3.13x10-3
2.60x10-3
2.08x10-3 1
frequency
period =

36. ,s 3 2 3 2
( 12)3
41.6
( 10.6)3
34.5
( 9.6 )3
29.7
( 8.0 )3
22.6
( 6.4 )3
16.2 l
, cm
( l )3

37. l tx10-3/s 4.0 Graph of 3.5 t against 3.0 2.5 2.0 1.5 1.0 0.5

38. Compare the graph with the equation a) c  0 Therefore the equation
gl3
a) t =
Therefore
the equation
is incorrect
General equation
y = mx
c = 0

39. l l tx10-3/s 4.0 Graph of 3.5 t against 3.0 2.5 2.0 1.5 1.0 0.5 /cm

40. Compare the graph with the equation b) c = 0 Therefore the equation E Al
b) t =
Therefore
the equation
is correct
General equation
y = mx
c = 0

41. Use the data above to confirm the choice of the right equation
Use the data above to confirm the choice of the right equation. Hence, determine the value of the constant A.
For steel: density  = 8500 kg m-3 ,
E = 2.0 x 1011 Nm-2  E Al
b) t =
m =
y = mx
3.91x10-3 s
12 cm  E
m = A
3.91x10-3 s
12 m
100 =  E = A =

42. Use the data above to confirm the choice of the right equation
Use the data above to confirm the choice of the right equation. Hence, determine the value of the constant A.
For steel: density  = 8500 kg m-3 ,
E = 2.0 x 1011 Nm-2  E Al
2.0 x 1011
b) t = = A
y = mx
A = 1.58 x 102  E
m = A  E = A

43. Example :
The dependence of the heat capacity C of a solid on the temperature T is given by the equation :
C = T + T3
What are the units of  and  in terms of the base units?

44. All the terms have same unit Unit for C = J K-1
Solution :
C = T + T3
All the terms have same unit
Unit for C =
J K-1 2
K-1
kg m s-1 =
= kg m2 s-2 K-1
Unit for T =
= kg m2 s-2 K-1
kg m2 s-2 K-1
unit for T
kg m2 s-2 K-1 K
Unit for  = =
= kg m2 s-2 K-2

45. Solution :
C = T + T3
All the terms have same unit
Unit for T3 =
= kg m2 s-2 K-1
kg m2 s-2 K-1
unit for T3
Unit for  =
kg m2 s-2 K-1 K3 =
= kg m2 s-2 K-4

46. Example :
A recent theory suggests that time may be quantized. The quantum or elementary amount of time is given by the equation : h
mpc2
T =
where h is the Planck constant,
mp = mass of proton and c = speed of light.
What is the dimension for Planck constant?
Write the SI unit of Planck constant.

47. Solution : h
mpc2 a)
T =
h =
Tmpc2
[ ] [ ]
h =
Tmpc2 T M
(L T–1)2 = =
M L2 T–1
Unit =
kg m2 s-1