Derivation of q(t) of Charging RC circuit

Obtained from HERE

Rotational Energy + Transitional Energy

Here comes the trick, emphasize that I got it myself but I'm not sure it's right or wrong. Rolling is regarded as a motion that combines linear motion together with rotational motion, but where does it hold? It holds everywhere in the universe, then why I so damn hate it?... If it holds everywhere then just seperate them and calculate. The problem is they are interchangable, and in many damn ways.

1) What happens when a very fast spinning object is placed on a frictionless ground?
It doesn't move but just spins on it's original position

2) What happens when a very fast spinning object is placed on a rough ground?
It spins very fast initially and gradually slows down spinning and start moving, why is it so?

Pure E(Rot) >
Rub Against the ground (Kinetic Friction) energy lost >
The (Rot) slows down due to frictional torque exerted >
(Lin) speeds up due to frictional force >
Eventually V(Lin) = (Omega)R and will be like that and keep on balancing on this point until the 2 energies fade out TOGETHER. Maybe if we look at the problem from 2 different directions the whole thing would be clearer.

Pure E(Lin) >
Rub Against the ground ( Kinetic Friction) energy lost >
The (Lin) slows down due to frictional force >
(Rot) speeds up because there is a torque due to the frictional force>
Eventually bla bla bla......and they keep balance out because as one of it creates kinetic friction it slows down and speeds up the other, releasing heat...

This happens at when we break suddenly while moving very fast or give the wheels a suddenly boost to 100 turns per second(imposible? possible...stupid!!)

Centripetal vs Centrifugal co-exists?

Rotational Motion

In order to maintain a circular motion, centripetal and centrifugal forces must equal, this we all know, but the concept is unclear, where comes this centrifugal force that appose the centripetal force. In the case of a roller coaster, it is R, but rotatioanl motion based on Strings and Gravity, what is the centrifugal force?.....

Here I have a case of a roller coaster, R-g= mv^2/r at bottom, R+g = mv^2/r at top, the 3 variables change accordingly when the roller coaster moves. I always tend to think that one of it is constant that makes the whole thing conplicated.

the R + g or R - g relation is actually the centripetal force and this centripetal force changes accordingly to mv^2/r, what is the main point here, AH HA !! Gravity doesn't change according to the centrifugal force, instead, gravity is always the same depend on what angle the coaster is at. So, gravity is the priority, and then there comes the centrifugal that is confusing. The R is CREATED by the CENTRIFUGAL FORCE to balance out everything, the track act as a essential element for this R to be adjusted, increase or decrease, and the CENTRIFUGAL FORCE will ONLY exist when ROTATIONAL MOTION is present, it looks LIKE newton's 3rd law, but not that intuitive. so at the top of the circle, if the coaster wants to keep on track, the minimum available centripetal force must be overcomed, and the minimum available is present, WHEN gravity is the only centripetal force<< why? because we cannot change gravity... and Thats it.

Petal = Fugal
R+G = mv^2/r

Simple Harnomic Motion

The Proof for the Simple Pendulum equation that I WANNA FIND FOR AGES!!

http://www.pa.msu.edu/courses/PHY191/exp5.pdf

Very useful Information

Here comes something to track down all the activities you do on your computer. Check WHETHER YOU WASTE YOUR LIFE !!
http://www.makeuseof.com/tag/manage-and-monitor-your-application-usage-with-manictime/

The one guide that I am searching for my whole life-.- !!

http://www.makeuseof.com/tag/5-easy-to-use-freeware-video-converters/


The following topics available in www.makeuseof.com in PDF format, very nice for beginners.

• The Internet Music Guidebook
• Twitter: Best Practices and Tips
• The Incredible Free Manual For Every Mac User
• Awesome Guide for the Internet Movie Addict
• Guide to the Biggest File Sharing Networks
• Underground Guide to the iPhone
• Ultimate Guide to Your Windows Mobile Phone
• How to Build a Great Media Center for Your Home
• A Computer Geek’s Smart Productivity Guide
• Easy Guide to Computer Networks
• A Newbie’s Initiation to Linux
• Big Book of BitTorrent
• An Idiot’s Guide to Photoshop
• Big Book of iTunes
• Idiot’s Guide to Building Your Own Cheap Computer
• Laptop Buying Guide of 2009
• PSP Down- and Upgrading Guide

http://www.makeuseof.com/makeuseof-downloads/#movieguide

C Language


char strNames[256];

scanf("%d", &a);

//this 2 functions cannot be used after scanf because the scanf will post a newline character after execution and gets or fgets will regard it as an input and hence will not prompt for input.

gets(a);
fgets(a, strlen(a), stdin);


18.02 Electriciry and Magnetism L04

Electrostatic Potential The amount of work that I need to do to move a single charge from very far away, to that particular point near the source of electric field, which gives the following V = kq/r or from another point of view, the work required to move a single charge from the 2 points V1 - V2 = W/q or from another point of view, the (distance moved x Force required to move a single charge) V1 - V2 = (F / q) d Electric Energy eV from W = qV, we get Energy = Coulombs x Work per Coulombs for a single electron or proton, 1 coulomb = 1.6 x 10^-19 = e so the Electric Energy of a accelerating electron can also be given by Ee = eV = 1/2 mev^2 Conservative Field As long as the difference in altitude is the same, no matter what weird path taken, the energy obtained by moving from this altitude, to the other altitude is the same,. Equipotential Surfaces Why a conductor has equipotential everywhere on it? When initially, a charge is introduced to the conductor, of course, there will be an electric field that disrupts the equipotential as the charge will generate an electric field and cause all the electrons to move around, running from high potential to low potential, UNTIL the electrons reaches a state where it is in its lowest potential, ( for electrons this should be highest potential available), by that time, the potential within the conductor should be everywhere zero. thats when we get E = 0 V= Constant

E&M - Electric Flux - Gauss's Law - Examples

3 Types of symmetrical assumption for electric field.

1) Electric field inside a conducting sphere that is perfectly round is zero.
Proof : Using Gauss's Law, set a charge within the sphere, the electric flux coming out from the sphere is a constant, 
8.02.L03.14.00

2) Elecrric field outside a conducting sphere that is perfectly round is same as having a charge at the center of the sphere.
3) Electric field that is between 2 conducing plates that is infinitely large is constant, the electric field near the edges is not zero, or if the ratio of the distance between the 2 plates and the area of the plates is too small.

Semiconducting Elements

Transistors

MOSFET
Here we are investigating the VI relation of a transistor using the MOSFET, from the below statement from wikipedia, we get the idea of the current being constant and the resistance of the transistor increases treamendously when the voltage increases, this effect still follow ohm's law's equation V = IR but in a special way that R is changing.

Power MOSFETs are at risk of thermal runaway. As their on-state resistance rises with temperature, if the load is approximately a constant-current load then the power loss rises correspondingly, generating further heat. When the heatsink is not able to keep the temperature low enough, the junction temperature may rise quickly and uncontrollably, resulting in destruction of the device.

P Type and N Type Semiconducting Materials

Is P Type Material positively charged?
Neutral unless you put static electricity onto it. P refers to the fact that conductivity comes from moving holes, which are positive but the electrons have not been removed from the material, they are just being held in the doping material. Having a doped material that conducts does not mean there is charge within the material, the amount of electrons and protons are still the same, just there are valence electrons floating around or vice versa....
http://in.answers.yahoo.com/question/index?qid=20070208022909AAGkOdU


Depletion Region of PN Junction Diode
http://www.ece.utep.edu/courses/ee3329/ee3329/Studyguide/Shockwave/PNjunctions/Demos/PNJunctionDiode.html#

Graphing Software

Geogebra - 2D graphing and analysis
http://www.geogebra.org/webstart/geogebra.html

Virtual Oscilloscope - Web Based mouse controlled virtual CRO
http://www.virtual-oscilloscope.com/help/x-y_button.html

Virtual CRO - Command Line virtual CRO, buggy
search at google

Lissajous Figure Simulation - Java Applet
http://lectureonline.cl.msu.edu/~mmp/kap23/Oscilloscope/app.htm

created my own Lissajour Figures in Geogebra

Website that has loads of lists of electrical component simulations

http://www.educypedia.be/electronics/javameasurement.htm

Moment of Inertia

Rotational Kinetic Energy :

Derived from Linear Kinetic energy :

EK = 1/2 mv^2 = 1/2 [m(r^2)](w^2) ------------> angular speed does not change within whole rigid body
Moment of Inertia is defined as
I = mr^2

MIT OCW Walter Lewin 8.01 L03 Fall 1999

Two Shortcuts to ease the finding of Moment of Inertia of an object

1) plugin another axis and I = Icenter + m d^2 where d is the distance between the center axis and the plugged axis

2)

Rotational Kinetic Energy can be stored in flying wheel for coverting into useful forms of energy when applicable. Eg : Toy cars, Neutron Star, earth, huge flying wheel in MIT magnetic labs

Vector, Forces

The Dot Product of a vector represents the scalar quantity of the combined vector, theoritically, only when 2 vectors of the same magnitude and opposite direction will cancel each other just like in forces, but according to the
A = ai + bj
B = ci + dj
a*b + c*d = |A||B|cosC

when angle C becomes 90 degrees, the Dot Product will become zero, what does this actually mean? the magnitude of the combined vector becomes zero? or the two vectors does not influence each other?
If the two vectors does not influence each other, why vectors without an angle of 90 degrees can be calculated to get a magnitude since they can be seperated into the x and y axis also.?

From my point of view, I think that the flaw of the vector rule lies at the interchanging of sides of the triangle when the angle becomes 90 degrees, cosine is no longer the case at this particular point, instead tangent should be used to obtain the actual angle and magnitude. Or maybe, tangent is the ultimate solution for the angle and the pathagoreom theorem is the ultimate solution for the magnitude by having to seperate everything into x,y,z axis beforehand.

After reviewed the material from MIT OCW, multivariable calculus lecture 1, The application of the vector is just to obtain the angle of 2 vectors and determine whether 2 vectors are perpendicular to each other, in that sense, the vector theorem has no flaws at all. There is still a struggle of the value obtained for |A||B|cosC, they said it is a scalar value, scalar value in the sense of what? two vectors of the same magnitude and direction cannot even add up with each other by using the dot product.

Answer :

So, that means geometrically, my two vectors are going more or less in the same direction. They make an acute angle. It's going to be zero if the angle is exactly 90°, OK, because that's when the cosine will be zero. And, it will be negative if the angle is more than 90°. So, that means they go, however, in opposite directions. So, that's basically one way to think about what dot product measures. It measures how much the two vectors are going along each other.

Quoted from MIT OCW 18.02 fall 2007

The meaning of DOT PRODUCT of 2 2D vectors, to determine how much a component A goes along component B, normally we compute this by setting component B as a unit vector so it does not causes any disturbance in the process.

Application of DOT PRODUCT
1) obtain angle between 2 vectors
2) Check whether 2 vectors are perpendicular to each other
3) determine the how much does component of Vector A goes along Vector B
4) Area of a parallelogram = |A| |B| sinC proven by base x height, | A || B | sinC = | A' || B | cos (90-C) = A ' . B = det (A, B)

Det(A,B,C) = + - Volume of parallelepipe

CROSS PRODUCT - L02 33.00
cross product of 2 vectors in 3D space
Definition : A x B = | i j k |
| a b c |
| d e f |
Definition : | A x B | which is the length of vector A and B = area of parallelogram formed by vector A and B

From 8.01 L03 fall 1999, Professor Lewin mention that the magnitude of The cross product is simply | A || B | sin C and the direction is just perpendicular to vector A and B, that clears the mystery of why length of A x B will equal to area of a parallelogram.


Application of CROSS PRODUCT
1) |A x B| = Area of parallelogram
2) dir (A x B) = Combined VectorAB that weirdly follows the right hand rule and goes along the third axis that is perpendicular to vector A and vector B.
Right Hand Rule => a) hand point along direction of A b) fingers point towards the direction of B c) the direction the thumb points is dir (A x B).

Geometrically, drawing A B C and using base x height, we get A . (B x C)
finally we check that,

Det(A,B,C) = A . (B x C)
for the full explaination refer to
18.02 L02 52.28

Extending the Applications
if the third vector C is parallel to the plane of AB we get,
C x (A . B) = 0
means that the volume obtained by taking the triple scalar product is zero.
N = A x B , which N is the vector perpendicular to the plane AB
C . ( N ) = 0, which C has no components, or is perpendicular along N

Matrix that turns the plane 90degrees clockwise or anticlockwise
| 0 -1 |
| 1 0 |

Capacitance, Inductance, Impedence, Reactance

http://www.ndt-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/impedance.htm

How many Types of Force are there in a classical mechanical system?

Real Forces (Forces that must be considered first)
1) Pressure
2) Tension
3) Gravitational Force
4) Frictional Force (Results from pressure that causes surface molecules to collide)

Imaginary Forces (Exists only because real forces exist)
1) Derived Forces (Gravitational Force must be seperated into 2 directions at a frictionless slope, and itself perished)
2) Centripetal Force

Opposing Force (Must act on different objects and must be opposite in direction)
1) Pressure - Pressure
2) Tension - Tension
3) Gravity - Attract - Attract
4) Friction - Rub - Rub

Will an astronaut feel an opposing force if
he stands on the ground and pushes an orange?
he floats in space and pushes an orange?
he floats in space and pushes the moon?
He wont feel an opposing force when he is at space, but he will accelerate at the opposite direction of the force he apply, which maybe will make him think that he successfully pushes the moon.

External Force and Internal Force
1) External Force is the force that is not paired up within the system, and will eventually cause the system to accelerate or if the external forces sum to 0, the system stays still.
2) Internal Force will never cause any changes to the "SYSTEM", in terms of displacement, velocity, acceleration, or energy.
3) If something does not move or is in an equilibrium, the external force must always be 0. (Applies even to water)[Pressure and Gravity is the 2 forces that shapes all liquids]

Physic Questions

External Force is the force that is not paired up and thus is the only one that can make the system suffer changes, or maybe not suffer changes if the dot product of the external forces sum to 0.

Gravitational Force MUST BE CHANGED to 2 resultant force at a frictionless slope,
ORIGINAL Gravitational Force MUST BE DELETED.

 Why vectors and trigonometry can be apply to Forces, Acceleration, Velocity, Displacement?
They are all derived from Displacement, which is metres. (PERSONAL OPINION)

What keeps us standing?
Gravity and pushing force from ground which sums to 0.

What keeps water surface constantly parallel to xxx?
Gravity + pushing force from water molecules that sums to 0.

Why water going down a slope will become diagonal?
the pushing force of water molecules at the direction of motion becomes 0.

If an astronaut pushes the moon/an orange in space, will he feel pressure?

What is the cause that we feel our own weight?
We dont feel our own weight, we feel the pressure exherted by the ground to our feet.

What actually increases when the lift rises up with an acceleration?
The force used to push us up is increase, our weight does not, the resultant force

Force and Motion

These kind of questions always frustrate me.

The upper scale shows 5N Initially, and when 5N of force is exherted at the bottom, the upper scale shows a reading of 5N but the lower scale shows a reading of 10N. Why is it so?

For these type of problem,
1)Every force across one rolling wheel as an individual force.
2) Newton's Third Law when a string is pulling something
3) Seperate everything you can into free body diagrams.

Fundamentals of rolling wheels,
1) A 180degree pull with one rolling wheel ----> Force does not change, only changes direction
2) A 0degree straight pull with the string at the other end attach to something, draw out all the forces individually and consider the total force at each direction. (Dirty Trick : use logic to find out the factor of the length of the string to be pulled compared to a 180degree pull)

Dot, Line, Plane, Body

What can we actually represent with 1D,2D and 3D?

For 1 Dimension,
1 Axis
1 Dot = Dot on a line
2 Dot = Line on a line

For 2 Dimension
2 Axis
1 Dot = Dot on a plane
2 Dot = Line on a plane
>= 3 Dot Area on a plane

For 3 Dimension
3 Axis
1 Dot = Dot on a Body
2 Dot = Line on a Body
3 Dot = Area on a Body
>=4 Dot = Volume on a Body

AC Circuit Analysis, RL,RC,RLC circuits

Impedence (Z)
A way to represent the reactance + resistance in an ac circuit in order to do calculations for V=IR
Note : j stands for imaginary (square root of -1)

RC circuit :
Z = 1/RCw j
RL circuit :
Z = 1/RLw
RLC circuit :
[to be added]

There are many ways to represent V=IR in an ac circuit Z are always used to replace R in ac circuit analysis and the calculation of the imaginary part is always seperated from the calculation of the real part.

1) V = Vmax [cos(wt + x)+sin(wt+x)]
2) V = ax + b
3) V = Vmax (e^(wt+x))
4) V = Vmax _wt+x

Kirchoff's Rule, Superposition, Thevenin's and Norton's Theorem

I was in this PALSI meeting where senior students guide the freshmens on homework and everything, trying to understand the connection between these 4 rules when people are trying to say, " Its enough that you know how to do it, just learn how to do it and get the right answer.". I was like "WTF? Are you guys even learning physics at all?"

It took me quite not a few hours to prove that they are related in some manner.

Kirchhoff's Rule is powerful enough to solve almost all circuits with batteries and resistors, how about if a current source is present?

From "Basic Electronics For Scientist" I get to know that alot of the formulas we get will stack with each other, so we must any how determine which one is useless and eliminate it. A common way to get through this is not to loop 2 loops individually that originate from the same battery

We just ignore the current source when we are calculating Total V in a specific loop, any current source that is encountered can be ignored.

200V = 47I3 + 4I1 + 23R4

And for The 2nd law of Kirchhoff where current never changes at any Nodes,
20A + I1 = I4