8.0.0. PHYSICAL QUANTITIES:
Physical quantities are properties of a substance or phenomenon that has a magnitude that can be determined and expressed from a reference point.
CLASSIFICATION OF PHYSICAL QUANTITIES
Physical quantities are classified into two:
1. Fundamental Quantities:
Fundamental Quantities are basic quantities that do not depend on any other quantity. They are quantities that can not be defined intern of any other quantity. They are quantities that other quantities depend upon for their derivations.
Fundamental Units:
These are units of the fundamental quantities.
Examples of Fundamental Quantities, units and their symbols
S/N Name of Quantity Name of Unit of Quantity Symbol of Unit
1 Length Meter m
2 Time Second S
3 Mass Kilogram Kg
4 Electric Current Ampere A
5 Temperature Kelvin K
6 Amount of substance Mole Mol
Derived Quantities:
Derived Quantities are those quantities that are derived or obtained from the fundamental quantities. They are dependent quantities that depend on the fundamental quantities for their derivations.
Derived Units:
Derived units are the units of derived quantities. They are derived from the combination of the fundamental units.
Examples of derived quantities, their units and symbols
S/N Name of Quantity Name of Unit of Quantity Symbol of Unit
1 Speed Meter per second m/s
2 Velocity Meter per second m/s
3 Acceleration Meter per second square m/s^2
4 Density Kilogram Per meter cube Kg/m^3
5 Area Meter square m^2
6 Volume Meter cube m^3
7 Work Newton meter Nm
8 Momentum Kilogram meter per second Kgm/s
9 Force Newton or kilogram meter per second square N or kgm/s^2
10 Pressure Newton per meter square or kilogram per meter square N/m^2 or kg/ms^2
11 Impulse Newton second or kilogram meter per second Ns or kgm/s
12 Frequency Hertz or per second Hz or 1/s
13 Resistance Ohm or volt per ampere ♎ or V/A
14 Plane angle Radian Rad
15 Solid angle Steradians Sr
16 Luminance Candela per square meter CD/m^2
17 Power Watt or joule per second W or J/S
18 Electric capacitance
19 Current density Ampere per meter square A/m^2
20 Specific volume Cubic meter per kilogram M^3/kg
21 Wave number Reciprocal of meter 1/m
22 Magnetic field strength
23 Electric charge
24 Potential difference
25 Momentum Kilogram meter per second Kgm/s
Derivation of units of derived quantities
I will use the following examples to show and explain how to derive the units of derived quantities. You must note that if a quantity has a formula or relation, then that quantity is a derived quantity.
For example,
1. the formula of speed is distance/time, therefore speed is a derived quantity
2. The formula of pressure is force/area, therefore pressure is a derived quantity. And so on in that same pattern.
Example 1:
Show that speed is a derived quantity.
Solution:
formula of speed is , speed or velocity = distance ÷ time
Distance is also called Length. Therefore distance is a fundamental quantity.
Its unit is meter and the symbol for meter is m.
Also, Time is a fundamental quantity, its unit is second and the symbol for second is s.
At this point, we replace distance with its unit which is meter ,symbol is m. We also replace Time with its unit which is second, symbol is s.
Therefore we will have,
Speed = meter (m) ÷ second (s) which becomes speed = m/s as the unit of speed.
We therefore say that the unit of speed is meter per second or m/s.
Example 2.
Show that acceleration is a derived quantity.
Solution :
formula of acceleration is , acceleration = velocity ÷ time
Remember that the formula of velocity is , velocity = distance ÷ time
Now, let us replace velocity with its own formula which is,
velocity = distance / time .
Then we will have,
acceleration = distance/time ÷ time .( Note we have replaced velocity with distance/time).
If we rearrange the formula, it will become
Acceleration = distance / time x time
Distance is also called Length. Therefore distance is a fundamental quantity.
Its unit is meter and the symbol for meter is m.
Also, Time is a fundamental quantity, its unit is second and the symbol for second is s.
At this point, we replace distance with its unit which is meter ,symbol is m. We also replace Time with its unit which is second, symbol is s.
Therefore we have,
Acceleration = distance / time x time , which will become
Acceleration = meter / second x second = m / s x s
Therefore the unit of acceleration is m / s^2
Example 3.
Show that pressure is a derived quantity.
Solution:
Pressure = force ÷ area
Formula of force is , Force = mass x acceleration , Acceleration = velocity / time
( unit is m/s^2). Unit of mass is kg.
If we multiply the unit of mass and acceleration , we will get
Unit of Force = kg x m/s = kgm/s
Formula of area = length x breadth ( length and breadth are distances, they are the same, they have the same units).
Unit of area = meter x meter = m x m = m^2
If we put the unit of force and the unit of area in the formula of pressure, then the unit of pressure will be,
Unit of pressure = kgm/s ÷ m^2 = kg/ms ( kilogram per meter per second)
Physical quantities are properties of a substance or phenomenon that has a magnitude that can be determined and expressed from a reference point.
CLASSIFICATION OF PHYSICAL QUANTITIES
Physical quantities are classified into two:
1. Fundamental Quantities:
Fundamental Quantities are basic quantities that do not depend on any other quantity. They are quantities that can not be defined intern of any other quantity. They are quantities that other quantities depend upon for their derivations.
Fundamental Units:
These are units of the fundamental quantities.
Examples of Fundamental Quantities, units and their symbols
S/N Name of Quantity Name of Unit of Quantity Symbol of Unit
1 Length Meter m
2 Time Second S
3 Mass Kilogram Kg
4 Electric Current Ampere A
5 Temperature Kelvin K
6 Amount of substance Mole Mol
Derived Quantities:
Derived Quantities are those quantities that are derived or obtained from the fundamental quantities. They are dependent quantities that depend on the fundamental quantities for their derivations.
Derived Units:
Derived units are the units of derived quantities. They are derived from the combination of the fundamental units.
Examples of derived quantities, their units and symbols
S/N Name of Quantity Name of Unit of Quantity Symbol of Unit
1 Speed Meter per second m/s
2 Velocity Meter per second m/s
3 Acceleration Meter per second square m/s^2
4 Density Kilogram Per meter cube Kg/m^3
5 Area Meter square m^2
6 Volume Meter cube m^3
7 Work Newton meter Nm
8 Momentum Kilogram meter per second Kgm/s
9 Force Newton or kilogram meter per second square N or kgm/s^2
10 Pressure Newton per meter square or kilogram per meter square N/m^2 or kg/ms^2
11 Impulse Newton second or kilogram meter per second Ns or kgm/s
12 Frequency Hertz or per second Hz or 1/s
13 Resistance Ohm or volt per ampere ♎ or V/A
14 Plane angle Radian Rad
15 Solid angle Steradians Sr
16 Luminance Candela per square meter CD/m^2
17 Power Watt or joule per second W or J/S
18 Electric capacitance
19 Current density Ampere per meter square A/m^2
20 Specific volume Cubic meter per kilogram M^3/kg
21 Wave number Reciprocal of meter 1/m
22 Magnetic field strength
23 Electric charge
24 Potential difference
25 Momentum Kilogram meter per second Kgm/s
Derivation of units of derived quantities
I will use the following examples to show and explain how to derive the units of derived quantities. You must note that if a quantity has a formula or relation, then that quantity is a derived quantity.
For example,
1. the formula of speed is distance/time, therefore speed is a derived quantity
2. The formula of pressure is force/area, therefore pressure is a derived quantity. And so on in that same pattern.
Example 1:
Show that speed is a derived quantity.
Solution:
formula of speed is , speed or velocity = distance ÷ time
Distance is also called Length. Therefore distance is a fundamental quantity.
Its unit is meter and the symbol for meter is m.
Also, Time is a fundamental quantity, its unit is second and the symbol for second is s.
At this point, we replace distance with its unit which is meter ,symbol is m. We also replace Time with its unit which is second, symbol is s.
Therefore we will have,
Speed = meter (m) ÷ second (s) which becomes speed = m/s as the unit of speed.
We therefore say that the unit of speed is meter per second or m/s.
Example 2.
Show that acceleration is a derived quantity.
Solution :
formula of acceleration is , acceleration = velocity ÷ time
Remember that the formula of velocity is , velocity = distance ÷ time
Now, let us replace velocity with its own formula which is,
velocity = distance / time .
Then we will have,
acceleration = distance/time ÷ time .( Note we have replaced velocity with distance/time).
If we rearrange the formula, it will become
Acceleration = distance / time x time
Distance is also called Length. Therefore distance is a fundamental quantity.
Its unit is meter and the symbol for meter is m.
Also, Time is a fundamental quantity, its unit is second and the symbol for second is s.
At this point, we replace distance with its unit which is meter ,symbol is m. We also replace Time with its unit which is second, symbol is s.
Therefore we have,
Acceleration = distance / time x time , which will become
Acceleration = meter / second x second = m / s x s
Therefore the unit of acceleration is m / s^2
Example 3.
Show that pressure is a derived quantity.
Solution:
Pressure = force ÷ area
Formula of force is , Force = mass x acceleration , Acceleration = velocity / time
( unit is m/s^2). Unit of mass is kg.
If we multiply the unit of mass and acceleration , we will get
Unit of Force = kg x m/s = kgm/s
Formula of area = length x breadth ( length and breadth are distances, they are the same, they have the same units).
Unit of area = meter x meter = m x m = m^2
If we put the unit of force and the unit of area in the formula of pressure, then the unit of pressure will be,
Unit of pressure = kgm/s ÷ m^2 = kg/ms ( kilogram per meter per second)
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