Fundamental quantities
Fundamental quantities are the basic quantities that are independent of other quantities.
They cannot be defined in terms of other quantities or derived from them.
Most of the derived quantities depend on them. Examples of fundamental quantities are Length, Mass, Time, Temperature, Electric current, Amount of substance, and Luminous intensity.
Note: The three most important basic quantities in Physics are length, mass, and time
Fundamental Units
Fundamental units are the basic units upon which other units depend. They are the units of fundamental quantities.
Examples of fundamental units are
meter (m), kilogram (kg), seconds (s), kelvin (k), ampere (A), mole (mol), and candela (cd).
Fundamental quantities and their units
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Fundamental quantities
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Units
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Symbols
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|
Length
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meter
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m
|
|
Mass
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kilogram
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kg
|
|
Time
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seconds
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s
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|
Temperature
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kelvin
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k
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|
Electric current
|
ampere
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A
|
|
Amount of substance
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mole
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mol
|
|
Luminous intensity
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candela
|
cd |
Derived quantities
Derived quantities are quantities that are obtained by a simple combination of the fundamental quantities.
Examples of derived quantities are Area, Volume, Density, Velocity, Acceleration, etc
Derived unit
Derived units are obtained by a simple combination of fundamental units.
Examples of derived units are square meter (m2), cubic meter (m3), kilogram per cubic meter (kgm-3), etc
Differences between Fundamental and Derived Quantities
Fundamental quantities
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Derived quantities
|
|
1. They are generally accepted
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They are just accepted
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2. They are based on an international system
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They are formulated from the international system
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3. They can stand alone
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They cannot stand alone
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4. They have direct calculations
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Their calculations are derived
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5. They are basic units of measurement
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They are not basic units of measurement |
Difference between Fundamental and Derived Units
Fundamental
units
|
Derived units
|
|
1. They are standard
units of measurement
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They are not standard
units of measurement
|
|
2. They are generally
accepted all over the world
|
Not all are generally
accepted all over the world
|
|
3. They form the basis of
measurement
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They are not the basis
of measurement
|
|
4. They are accepted by
international organizations
|
Though accepted
internationally, they are formulated by individuals
|
|
5. They are known as S.I.
units, i.e. international system
|
They are known as units
|
Submultiples of units and their prefix
Multiples of units and their prefix
1. Convert the following to a meter
(a) 25cm
(b) 15mm
(c) 30km
2. Convert the following to square-meter (m2)
(a) 2mm2
(b) 20mm2
(c) 66cm2
(d) 70km2
3. Convert the following to grams(g)
(a) 10mg
(b) 50kg
4. Convert the following to seconds (s)
(a) 13minutes
(b) 20 hours
(c) 15 milliseconds
5. Convert the following to meter per second (ms-1)
(a) 36kmhr-1
(b) 108kmhr-1
(c) 108kmmin-1
(d) 108mhr-1
MEASURING INSTRUMENTS
Measuring instruments are tools used in physics or the field of science for getting the exact measurement of an object.
Examples of instruments used for measuring include
•Verner caliper
•Micrometer screw gauge
•Thermometer
•Voltmeter
•Ammeter
•Measuring cylinder
•Manometer
•Barometer etc
Mass
Mass is defined as the quantity of matter in an object. The S.I. unit of mass is kilogram (kg).
The instruments used to measure mass include
1. Chemical balance
2. Beam balance
3. Lever balance
4. Dial balance
5. Direct reading balance etc
Weight
Weight is defined as the force of gravity on an object. The S.I. unit of weight is Newton (N). The instrument for measuring weight include
1. Spring balance
2. Hydraulic scale
Differences between mass and weight
|
Mass
|
Weight
|
|
1. Mass is the quantity of matter in an object
|
Weight is the force of
gravity on an object
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|
2. Mass is constant
at any place and any time
|
The weight of
an object depends on the gravity at that place
|
|
3. Mass is a scalar
quantity
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Weight is a vector
quantity
|
|
4. Mass is a fundamental
quantity
|
Weight is a derived
quantity
|
|
5. Mass is expressed
in kilograms
|
Weight is expressed
in Newton
|
|
6. Mass is measured
using a beam balance
|
Weight is measured
using a spring balance
|
Length
Length is defined as the distance between two points along an object. The S.I. unit of length is a meter (m).
The instrument for measuring length include
1. Meter rule
2. Vernier caliper
3. Micrometer screw gauge etc
Time
Time is defined as a measure of the duration of an event. The S.I. unit of time is second (s).
The instrument for measuring time include
1. Stopwatch
2. Stopclock
3. Hourglass (Sandclock)
4. Atomic clock
5. Ticker tape timer
6. Wristwatch
7. Simple pendulum
8. Heartbeat
9. Electric clock etc
Volume
Volume is defined as the amount of space occupied by a matter. The S.I. unit of volume is cubic-meter (m3)
The instrument for measuring volume include
1. Burette
2. Pipette
3. Measuring cylinder
4. Volumetric flask
5. Eureka can etc
READING ACCURACY
The reading accuracy of a measuring instrument is the accurate or error values at which measurements can be made on that instrument
Instruments and their reading accuracy
|
Instrument
|
Reading accuracy
|
|
Stopwatch
|
0.1s
|
|
Meter rule
|
0.1cm
|
|
Vernier caliper
|
0.01cm
|
|
Micrometer screw
gauge
|
0.001cm
|
|
Beam balance
|
0.001g
|
Vernier caliper
Vernier caliper is used to measure
1. Internal and external diameter of a tube
2. Diameter of a circular object
3. Thickness of an object
Example 1: What is the reading on the vernier caliper?
Vernier scale. = 0.04cm
Vernier reading = 3.3 + 0.04
= 3.34cm
Example 2: What is the reading on the vernier caliper?
Vernier scale = 0.08cm
Vernier reading= 2.8 + 0.08
=2.88cm
Micrometer screw gauge
The micrometer screw gauge is used to measure smaller dimensions than the vernier caliper.
It is used to measure
1. The diameter of a circular object e.g. Wires
2. Thickness of paper etc
Example 1: What is the reading on the micrometer screw gauge?
Vernier scale= 0.21mm
Measurement reading = 3.0 + 0.21
= 3.21mm
Example 2: What is the reading on the micrometer screw gauge?
Main scale = 5.5mm
Vernier scale= 0.42mm
Measurement reading = 5.5 + 0.42
= 5.92 mm
ASSIGNMENT
1. Explain the following
a. Accuracy
b. Precision
c. Parallax error
2. What is the meaning of the S.I. unit?
3. State the instrument for measuring the following
a. Length of a simple pendulum
b. Diameter of a metal rod
c. Thickness of the central portion of a thin lens
d. Outer and inner diameters of a tube
e. The diameter of a small spherical bob
4. Draw a label diagram of the following instrument
a. Chemical balance
b. Spring balance
c. Verner caliper
d. Micrometer screw gauge
e. Stop clock
f. Measuring cylinder
5. State the reading on the following instruments
a.
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