1.1physical quan��es and measurement techniques
- length is measured in km, m, cm, mm…….
- in SI system, length is measured in meters.
- we use a ruler to measure length and for small lengths we use a tool called micrometer screw gauge.
- �me is measured in years, months, weeks, hr, min, sec…….
- in SI system, �me is measured in seconds.
- remember that: 1hr = 60 min,
1min = 60 s,
1hr = 3600 s
- we use stopwatches to measure �me.
- to measure small �mes, such as �me of fast vibra�ons, we measure the total �me of 10 or 20 oscilla�ons
then divide it by the number of these oscilla�ons.
- we can classify physical quan��es in to scaler or vector quan��es.
- a scaler quan�ty is completely described by its magnitude (value). E.g. (distance, speed, mass, �me,
temperature, ……etc).
- a vector quan�ty is described by its magnitude and direc�on. E.g. (displacement, force, velocity,
accelera�on, moment, ……, etc).
- Distance and displacement:
* Distance is a value describing the path length between two points of an object without any regard to
direc�on.
Distance is a scaler quan�ty.
* Displacement is the shortest path between two points (a straight line sta�ng from the beginning point
and terminates at the end point)
Ex., a car moved to the east 6m and then to the north 8m, calculate the distance and displacement of the
car?
Star�ng point
end point
Distance = 6+8 = 14m
8m
displacement = 10m northeast
6m
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Ex., based on the adjacent figure, an object started moving
from point A to point B, and then from point B to point C,
calculate the distance and displacement of the object, what do
you no�ce?
A
10m
B
9m
C
Distance = 10+9 = 19m
Displacement = 19m, east
Conclusion: distance = displacement (as a magnitude) if the object moves in a straight line in the same
direc�on.
Scaler
Distance
Speed
Mass
Energy
Temperature
Time
Vector
Displacement
Velocity
Weight
Note that some victors and scalers are similar to
each other
Force
Accelera�on
Momentum
Electrical field
- Area
- it is measured in m2 in SI system.
r
Breadth
height
(width)
Length
A = length × breadth
base
A=
1
2
× base × height
A = πr2
2
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Ex., depending on the figure, find the total area?
A1 =
1
2
1
× base × height = 2 × (3×10-2) × (2×10-2) = 3×10-4 m2
2
A2 = length × breadth = (3×10-2) × (2×10-2) = 6×10-4 m2
2cm
2cm
3cm
A = A1 + A2 = 3×10-4 + 6×10-4 = 9×10-4 m2
- Volume
- the amount of space occupied.
- it is measured in m3 in SI system.
- the volume of some uniform shapes:
Cube
Rectangular block
x
height
x
Length (x)
Vc = (length)3
Length
breadth
Vr = length × breadth ×
Ex., a block of wood has a rectangular shape, it is 4 cm in long, 10 cm in height, 3 cm in thickness,
calculate its volume.
V = length × breadth × height = (4×10-2) × (10×10-2) × (3×10-2) = 1200 × 10-6 m3 = 0.0012 m3
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Cylinder
Cross sec�on area (base area)
r
height (h)
Vcy = base area × height
Vcy = πr2h
Ex., what is the volume of a cylinder of radius of 10 mm and height of 5cm?
Vcy = πr2h = 3.14 × (10×10-3)2 × (5×10-2) = 3.14 × (100×10-6) × (5×10-2) = 1570×10-8 m3= 0.00001570 m3
- measuring cylinder
- it is used to measure the volume of a liquid and can be used to measure the volume of irregular shaped
solid objects.
The eye must be leveled with the botom of the curved liquid (meniscus) (for mercury it would be the
top of the curve).
Measuring cylinders are o�en marked in millilitres (ml) where 1 ml = 1 cm3.
Note that 1000 cm3 = 1 dm3 (= 1 litre).
water
mercury
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- Significant figures
significant figures: The number of figures (digits) given for a measurement indicates how accurate we
think it is and more figures should not be given than are jus�fied.
Rules to iden�fy significant figures in a number
1) Non-zero digits within the given measurement are significant.
2) Zeros between two significant non-zero digits are significant.
3) Zeros to the le� of the first non-zero digit (leading zeros) are not significant.
4) Zeros to the right of the last non-zero digit (trailing zeros) in a number with the decimal point are
significant if they are within the measurement.
- When doing a calcula�on your answer should have the same number of significant figures as the
measurements used in the calcula�on.
- in deciding the least significant figure you look at the next figure to the right of it.
1) If it is less than 5, you leave the least significant figure as it is.
for (3) significant figures 21.34 becomes 21.3
2) if it equals or is greater than 5 you increase the least significant figure by 1 (round it up).
for (3) significant figures 21.36 becomes 21.4
- parallax error
An error caused by not taking the reading from some devices (like rulers and mechanical gauges)directly
over the mark.
Fig. 1.1.2 Page 3
In rulers this error is cause by the thickness of the ruler
In mechanical gauges it is caused by the gap between the needle and the marks.
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