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

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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