Physical quantities, units & measurements complete
1. PHYSICS
“The branch of science which deals with the study of matter, energy &
the interaction between them.”
PHYSICAL QUNATITIES:
Those quantities which can be measured are called physical quantities.
For example: Length, mass, time, acceleration, momentum etc.
NON-PHYSICAL QUANTITIES:
Those quantities which cannot be measured are called non-physical
quantities.
For example: Like, Wish, Sorrow, Hate, Love etc.
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2. FUNDAMENTAL QUANTITY
International system of units is based on seven independent
quantities known as fundamental quantities. These are given below:
PHYSICAL
QUANTITY
SYMBOL FOR
QUANTITY
UNIT SYMBOL OF
UNIT
Length l Meter m
Mass m Kilogram kg
Time t Second s
Electric current I Ampere A
Temperature T Kelvin K
Luminous
Intensity
Iʋ Candela cd
Amount of
substance
n Mole mol
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3. DERIVED QUANTITY
The physical quantities other than fundamental quantities are all
called derived quantities. For example:
PHYSICAL
QUANTITY
SYMBOL FOR
QUANTITY
UNIT SYMBOL OF
UNIT
Speed v Meter/second m/s
Acceleration a Meter/second2 m/s2
Volume V Meter3 m3
Force F Newton N
Pressure P Pascal P
Work W Joule J
Charge Q Coulomb C
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4. PREFIXES
Prefixes are very useful in expressing some quantities which are either
very small or very large.
For example: The distance between air molecules is 0.000 00001m, we
can also mention this by using prefixes i.e. 0.01 μm.
One more convenient way to express large or small quantities is
standard form i.e. in standard form, the distance between air
molecules is 1x10-8 m.
NOTE: When point is drag on right hand then power in standard form
is negative.
When point is drag on left hand then power in standard form is
positive. 10+
10-
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5. PRACTICE EXERCISE FOR STANDARD FORM
❶12000 000 m
❷0.000 000 0003 m
❸1000 000 kg
❹0.000 000 1 s
❺6400000 m
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6. PREFIXES
Terminology Symbol Value Numerical value
Pico p 10-12 0.000000000001
Nano n 10-9 0.000000001
Micro μ 10-6 0.000001
Milli m 10-3 0.001
Centi c 10-2 0.01
Deci d 10-1 0.1
Zero - 0 0
Deca D 101 10
Hecto H 102 100
Kilo K 103 1000
Mega M 106 1000000
Giga G 109 1000000000
Tera T 1012 1000000000000
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7. UNIT CONVERSIONS
Length
⎕m →
⎕
𝟏𝟎𝟎𝟎
km
⎕cm →
⎕
𝟏𝟎𝟎
m
⎕mm →
⎕
𝟏𝟎𝟎𝟎
m
----------------------------------------
⎕km → ⎕x1000 m
⎕m → ⎕x100 cm
⎕m → ⎕x1000 mm
Exercise:
Convert the following:
❶1000 cm to m
❷200 mm to m
❸50 km to m
❹500 m to mm
❺10 km to mm
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8. Mass
⎕g →
⎕
𝟏𝟎𝟎𝟎
kg
⎕mg →
⎕
𝟏𝟎𝟎𝟎𝟎𝟎𝟎
kg
⎕mg →
⎕
𝟏𝟎𝟎𝟎
g
------------------------------------------
⎕kg → ⎕x1000 g
⎕g → ⎕x1000 mg
Exercise:
Convert the following:
❶1000 mg to kg
❷50 kg to g
❸2 kg to mg
❹500 g to kg
❺10 mg to g
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10. SCALARS & VECTORS
SCALAR QUANTITY:
“Physical quantity which can only be specified by magnitude is called
scalar quantity.”
For example: Distance, Speed, Time, Length etc.
VECTOR QUANTITY:
Physical quantity which can be specified by magnitude as well as
direction is called vector quantity.”
For example: Displacement, Velocity, Acceleration, etc.
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11. DRAWING A VECTOR
Draw a vector of a velocity of 20 m/s in the
direction of N45°E.
STEPS:
• Choose an appropriate scale. In this case, we
may choose 1 cm to represents 5 m/s.
• The length of the arrow will represent the
magnitude of the vector. To represent a
velocity of 20 m/s using the above scale, the
length of the arrow would be 4 cm.
• Using protractor, measure an angle N45°E.
The arrow diagram is shown in figure.
Scale: 1 cm: 5 m/s
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12. ADDITION OF VECTOR(ALONG THE SAME STRAIGHT LINE)
By addition of vector, we mean a single resultant vector.
In figure A, two forces of magnitude 5 N & 3 N are acting towards right
so their resultant will be 8 N
In figure B, two forces of 2 N & 4 N are acting on left & right
respectively, their resultant is 2 N.
(A)
(B)
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13. HOME WORK
Q: Three forces 3 N, 1.5 N & 6 N act on a mass as shown in
figure. What is the resultant due to the three forces?
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14. METHODS OF ADDITION OF VECTORS
When the vectors making an angle with each other
rather then at the same straight line, then we use
methods of vector addition.
TIP TO TAIL RULE:
• Consider two vectors A & B.
• Join the head of vector A with the tail of vector B
without any change in magnitude & direction.
• Then draw a resultant vector R whose
magnitude is equal to the shortest distance
between tail of vector A to the head of vector B.
• The direction of the resultant vector R is directed
from the tail of vector A to the head of vector C
as shown in figure.
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15. PARALLELOGRAM METHOD
Consider two vectors 3 N & 5 N acting on a block
as shown in figure. (Not in same straight line)
To find the resultant force according to
parallelogram, we use following steps:
• Choose particular scale & draw forces using
arrows. Here arrow OA represents 5N &
arrow OC represents 3N forces.
• Complete parallelogram OACB such that AC is
parallel AB is parallel to OC & OA is parallel to
BC.
• The resultant of the parallelogram can be
drawn as a diagonal of the parallelogram OB
directed towards point B. the length of the
resultant is 7 cm which means resultant force
is 7 N with direction of 18°. Scale: 1 cm: 1 N
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16. MEASURING INSTRUMENTS (LENGTH)
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LENGTH INSTRUMENT ACCURACY
Several meters Measuring tape 0.1 cm
Several cm to 1 m Meter rule 0.1 cm
Between 1 cm to 10 cm Vernier callipers 0.01 cm
Less than 2 cm Screw gauge 0.01 mm
17. METER RULE:
The commonly used instrument to measure the length of objects such as
wires or distance between two points. It is best to measure from 1 cm mark
& then subtract 1 cm from final reading because of the wear & tear of zero
mark.
For accurate measurements, always place your eye vertically above the
mark to avoid parallax error.
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18. VERNIER CALLIPERS
The commonly used instrument to measure the length of objects up to 0.01
cm small.
Steps of reading vernier scale:
• Read the division on main scale which is just behind or on the zero of
Vernier scale (In our case it is 18.2 cm)
• Now see which division of Vernier scale coincides with the division of
main scale (In our case its 10)
• Now multiply that coincident division with the precision of Vernier
callipers.
CALCULATION:
Main scale div. + Vernier div. x (Precision)
18.2 + 10 x (0.01)
18.2 + 0.1
18.3 cm
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19. SCREW GAUGE
The commonly used instrument to measure the length of objects up to 0.01
mm small.
Steps of reading screw gauge scale:
• Read the division on main scale which is just last visible on the datum
line. (In our case it is 12 mm)
• Now see which division of Circular scale coincides with the datum line of
main scale (In our case its 40)
• Now multiply that coincident division with the precision of screw gauge.
CALCULATION:
Main scale div. + circular div. x (Precision)
12 + 40 x (0.01)
12 + 0.4
12.4 mm
20. MEASURING INSTRUMENTS (TIME)
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Due to wide range of time intervals we want to measure, we need different
types of measuring instruments.
We will be measuring time with:
• Stop watch
• Ticker tape timer
PERIODIC MOTION
Such a motion which repeats itself after a particular interval of time is
known as periodic motion.
E.g: motion of pendulum, spring etc.
Such repetitive motion is called OSCILLATION & the time required to
complete one oscillation is called PERIOD.
