Transcript Physics Lectures

1. Units and Quantities
Kamil Sarka
SI Units
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Length (meter: m)
Mass (kilogram: kg)
Time (second: s)
Electric current (ampere: A)
Thermodynamic temperature (kelvin: K)
Amount of substance (mole: mol)
Luminous intensity (candela: cd)
http://physics.nist.gov/cuu/Units/index.html
SI Derived Units (selected examples)
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Frequency (Hertz: Hz=1/s)
Force (Newton: N=m.kg/s2)
Pressure (Pascal, Pa=N/m2)
Energy, work, quantity of heat (Joule: J=n.M)
Power, radiant flux (Watt: W=J/s)
http://www.chemie.fu-berlin.de/chemistry/general/si_en.html
SI Prefices
Factor
Name
Symbol
10-1
Deci
D
1024
yotta
Y
10-2
centi
c
1021
zetta
Z
10-3
milli
m
1018
exa
E
10-6
micro µ
1015
peta
P
10-9
nano
n
1012
tera
T
10-12
pico
p
femto f
109
giga
G
106
mega
M
10-15
103
kilo
k
10-18
atto
102
hecto
h
10-21
zepto z
101
deka
da
10-24
yocto y
http://www.gordonengland.co.uk/conversion/xprefixconv.htm
a
Scalar and vector quantities
• Scalar
• Vector
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• Force
• Velocity
• Momentum
Mass
Heat
Temperature
energy
Philosophical question: Is time scalar or vector?
What is a vector?
Vector is concepted and characterised
by its magnitude and direction
Vector (lat.) ~ pusher, driver, carrier..
Addition of vectors
Angle =0°
Angle ≠0°
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l1b.html
Graphic method for vector addition
Resulting force
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=51
http://surendranath.org/Applets/Math/VectorAddition/VectorAdditionApplet.html
Vector addition (mathematically)
We can add only vector from the same euclidian spaces
B  (b1 , b2 ,..., bn )
A  (a1 , a2 ,..., an )
A  B  (a1  b1 , a2  b2 ,..., an  bn )
Vector addition (mathematically)
We can add only vector from the same euclidian spaces
b
c
c  a 2  b 2  2ab cos( )

a
Vector multiplication
dot product
n
a  b   aibi  a1b1 a2b2  ...anbn
i 1
cross product
i
j
k
u  v  ux
uy
uz
vx
vy
vz
http://mathworld.wolfram.com/Determinant.html
This is
calculated
like
determinant
Vector multiplication
dot product
c  a b cos( )
cross product
c  a b sin( )
The angle
between the
two vectors
a and b
http://mathworld.wolfram.com/Determinant.html
Vector multiplication
dot product
a bb a
cross product
u  v  v  u
http://mathworld.wolfram.com/Determinant.html
Derivative
The derivative of a function represents an infinitesimal change in the
function with respect to one of its variables.
s
r2 '
s2
s s
v 
t t
s1
t1
t2
t 2'
t
s ds
If t  0 then v  lim

t  0 t
dt
Integration
Integal can be interpreted as area under the curve (function)
s  v t
s   vi  ti
i
If
t  0 then s 
 v  t   v  dt
i
i
i
Thank you.