Download 1.1 Standards of length, mass time Speed = L/T SI Units

Ch1 Introduction.
1.1 Standards of length, mass time
SI Units
Length (m)
the distance traveled by light in vacuum during
a time interval of 1/299792458 second
Km =1000m
cm = 0.01 m
1 m = 39.37 in. = 3.281 ft
1 km = 0.621 mi
Mass (Kg)
the mass of a specific platinum iridium alloy
cylinder kept at the International Bureau of
Weight and Measures at Sèvres, France
1 Kg g= 2.20462 lbs(pound is a unit of force.)
Time(sec)
9 192 631 700 times the period of oscillation of
radiation from the cesium atom.
Speed = L/T
exception
Temperature.(K,T)
Charge(C, Q)
Guessing an equation by using dimensional
analysis
Acceleration equation
[a] = L/T2
[v] = L/T
[x] = L
a= v t
x=?
E = mc2 this famous equation can be guessed
from dimensional analysis.
[E] = M L2/T2 =[m c2]
Do not forget units when you write answers.
2300 2 or 4
Two main rules
In multiplying/dividing two or more quantities,
the number of significant figures in the final
product is the same as the number of significant
figures in the quantity which has the lowest
significant figures.
When numbers are added/subtracted, the
number of decimal places in the result should
equal the smallest number of decimal places.
examples
1.23 x 4.5 = 5.535
but the number of sig. figure should be 2, since
4.5 has the lowest sig. figure, 2
so the final answer should be
1.23 x 4.5 = 5.5
1.3 Dimensional analysis
1.4 Uncertainty in Measurement and Significant 1.23 + 4 = 5.23
Dimension: the physical nature of a quantity
Figures
but the smallest number of decimal places is 1,
L: length
significant figure is a reliably known digit.
so the final answer is
M:mass
1.23 + 4 = 5
certain
uncertain
8.65
T or t:time
However,
Dimensions of most physical quantities can be
1.23 + 4.00
written as the combinations of Length, Mass
in this case, the smallest number of decimal
and time.
places is 0.01, so the final answer is
1.23 + 4.00 = 5.23
Dimensions can be treated as algebraic
8.6
uncertain
certain
quantities. [] is often used to denote the
Scientific notation.
dimension of a quantity
How many significant figures each number has? It is not clear how many significant figures 4000
123 3
has. In this case, scientific notation is useful.
Volume = L3
1.23 3
A x 10n where 1<A<10
Area = L2
0.00011 (leading zeroes are not sig.)
Ch1
Distance between two points
11.5 Conversion of units
d  ( x2  x1 ) 2  ( y2  y1 ) 2
Conversion factors can be used to convert units
from one to another. In the conversion of units, Polar coordinate system
(r,θ)
the units are treated as algebraic quantities.
examples
Final unit
beginning unit 
 Final unit
beginning unit
10 MPH to m/s
10 miles / h x 1609 m /1 miles
=16090 m/h x 1 h/ 60 min x 1 min /60 s
=4.5 m/s
r
Define positive sides when you use it.
r
θ
Find x in terms of r and θ.
θ
This is useful when we study rotation.
1.8 Trigonometry
SOH-CAH-TOA
sinθ = opposite/ hypotenuse
cosθ= adjacent/ hypotenuse
1.6Estimation and order of magnitude
tanθ= opposite/adjacent
calculations
Order of magnitude calculation can be useful Pythagorean theorem
when you need a rough estimation of a quantity r2 = x2 + y2
Inverse function
45 ~ 10
θ = sin-1x
75 ~ 100
You can calculate the inverse functions by using
123567 ~ 105
calculator, but you need to careful about the
unit. The result can be in radian or degree,
1.7 Coordinate system
depending on the settings
Cartesian coordinate system
(x,y)
y
Examples
Example 1.10 in the text book.
x
x