Newtonian Physics: lesson 1 : Intro

[Fluffy]

Intro for the chapter:
-----------------------------------
Well I wanted to do something for the LLP in the knowledge side so I put my physics skills to the test and constricted an array of lessons that meant to teach you the basic of neotenic physic on non-rigid bodies ( maybe there will be an expansion).

When we talk about physics we generally distinguish between newtonian physics , electricity and modern physics. Electricity talks about the transportation of charged particles and the likes ( capacitors resistors , electrostatic electrodynamic etc) modern talks about modern theories (such as quantum physics and chaos theory).

newtonian physics talks about the basic form of physics. Its majorly deals with bodies and the way they "react" to forces being implied on them.

The Lesson

The first thing I need to explain is that i assume that you got some basic knowledge of vectors when reading these articles, If you don't know search wikipedia for the term vector in math and learn addition substraction and multiplication(both scalar and vector) of vectors.

I will start with pointing out the difference between a mathematical vector to physical one. While math say that any vector can be moved to any point while you don't change it's direction and size physics doesn't allow that. Thats comes form the fact that physical vector represent velocity(speed), acceleration,work , and way that was passed.



Kinematics

Kinematics is the part of physics that discuss about the movement of object and the way to predict there location,speed and acceleration at any given time we will approach this field only from the aspect of straight line movement (we can take non straight line movement and break it to 2-3 straight line movements).


I will start with explaining the terms of this field:
(term-letter marks the term in equations-definition-unit of measurements)

Location- x- the place where an object is relative to a ceratin point-meter .

Velocity(speed of object)-v- how much distance the body will go in one second- m/s (meter for second, mathematically a meter divide in a second)

acceleration- the amount of velocity units that the object will gain in one second-m/s^2(explanation in picture down).
[img:2c07a9b084]http://img240.imageshack.us/img240/6964/acc7ar.th.png[/img:2c07a9b084]

Well after explaining these terms I will explain the mathematical connection between them:

X- this is the basic unit to wich the other refer.
V- velocity is the amount of Location units "gained" in one time measurements , so I can say that Velocity to time graph-v(t)- is the deferential of the X(t) graph (t stands for time, counted in seconds)
explanation:
[img:2c07a9b084]http://img139.imageshack.us/img139/2194/def4kh.th.png[/img:2c07a9b084]

a- acceleration is the amount of velocity units "gained" in one second hence the graph of a(t) is the deferential of the V(t) graph).


After we understand this I can explain the basic 3 kinematics equations.

You can only use this equations if the acceleration is constant for the time you are referring

1) V0 is the velocity at a moment chosen as t=0.

[img:2c07a9b084]http://img4.imageshack.us/img4/6263/kena14ls.th.png[/img:2c07a9b084]

This equation is simple to explain. since the acceleration is constant the graph of v(t) is liner( if the deferential is constant it represent the slope of a liner graph).

since the graph is liner his equation is from the type f(x)=m*x+c ( c represent the initial value of f(x)). since our x is t (time in seconds) and the slope is the acceleration the equation is: v(t)=a*t+c . we already defined v0 as the initial value of v so in the end we get: v(t)=v0+a*t.

2)
[img:2c07a9b084]http://img114.imageshack.us/img114/2640/kena28dg.png[/img:2c07a9b084]

This equation is actually the representation of the "average velocity"*"time" . This gives the total way the object went since we know that velocity(speed)*time=way (basic algebra equation) .

now since the acceleration is constant we can conclude that the change rate of velocity is constant toward t( v(t) is liner).

Once we know that we can get the average velocity quite easily:
V(avg)={v0+v(final)}/2

now lets work on V(final):

since we know the time we can use the first kinematic equation: v=v0+a*t.

now lets put this in the v(avg) equation:

V(avg)=(v0+v0+a*t)/2
|
|
V
v(avg)=(2*v0+a*t)/2
|
V
v(avg)=v0+1/2*a*t

and now all we have to do to get the distance is multiply by t.

x=V(avg)*t=(v0+1/2*a*t)*t +x0
|
V

x=v0*t+1/2*a*t*t+x0
|
V

x=v0*t+1/2*a*t^2+x0.


3)
[img:2c07a9b084]http://img222.imageshack.us/img222/4786/kena38kh.th.png[/img:2c07a9b084]

This is the last (and the most complicated to explain) kinematic equation.

from the 2nd equation we know that X=x0+v(avg)*t.

now we know that since the acceleration is constant v(avg)={v+v0}/2.

hence we know that : x=x0+{[v+v0]/2}*t

now lets isolate t from the first equation:

v=v0+a*t
a*t=v-v0 /:a

t=(v-v0)/a.

now lets put this equation in the equation above:

x=x0+{[v+v0]/2}*{(v-v0)/a}

now lets play with this equation a bit:

x-x0={[v+v0]/2}*{(v-v0)/a}

x-x0={(v+v0)*(v-v0)}/2*a

now lets multiply in 2a to get rid of this division.

2a(x-x0)=(v+v0)(v-v0)

starting to look familiar right? .

now from basic algebra we can take the identity : (a+b)*(a-b)=A^2-B^2.
if we use it on our equation we get:

2a(x-x0)=v^2-v0^2.

lets switch the v0^2 side:

2a(x-x0)+v0^2=v^2

now lets switch sides so it will look like the equation in the picture:

v^2=V0^2+2a(x-x0)

Thats it .

---------------------------------------------------------------------------

Next Lesson:

Free Fall Movement and Vertical Throw.

( I have 14 Lessons in the series to make so keep in mind that it will be long. After all it does cover 1 year of high-school material)





-------------------------------------------------------------------------------

WOW this was long