Conservapedia - User contributions [en]

FBI Investigation

2007-09-05T15:44:38Z

Goldrod:

This page has been classified and is under investigation in accordance with the [[Patriot Act]]. To voice decent, please pick up your phone and speak directly into it. Include the codewords "I disagree with the government" and [[Echelon]] will take your call.

Gravitation

2007-09-05T15:42:42Z

Goldrod:

:''This page is over '''gravity'''. Gravity is a theory, '''not a fact'''. Information presented in this article should be critically interpreted and taken with an open mind. There are true challenges to this debated theory including the [[intelligent falling]] theory''.
'''Gravitation''' is a [[phenomenon]] which attracts all objects within the [[universe]] to each other <ref>New Oxford American Dictionary, 2nd Edition</ref>. In modern [[physics]], it is explained by the [[Theory of relativity|General Theory of relativity]]. Before general relativity, gravitation was described by [[Sir Isaac Newton|Isaac Newton's]] law of universal gravitation, which is still useful in most situations.

Everything in the universe that has mass attracts every other thing that has mass. How much depends on the size of the masses and the distance between them. For normal objects, this pull is minute, but you can measure the pull between a very large object like the [[Earth]] and another object like you by standing on the scales. Your weight is the measure of the pull of gravity between you and the planet you are standing on. This force depends on your mass and the mass of that planet, but it also depends on your distance from the center of the planet. The further you are from the planet's center, the weaker the pull between it and your body. If you double your distance, the force is one quarter. At ten times the distance, the force is one hundredth. It drops off with the square of the distance. This is called the [[Inverse Square Law.]] <ref>http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html</ref>The force never becomes zero, no matter how far you travel.

The law itself is stated as

:<math>F = G \frac{m_1 m_2}{r^2}</math>

Where the force due to gravity equals the mass of the first object, ''m''1, is multiplied by the mass of the second object, ''m''2, which is then divided by the distace between the center of mass of both objects, r, squared. This is then multipled by the [[gravitational constant]]: 6.67428x10-11 N m2 Kg -2

Gravitation is responsible for making objects accelerate towards each other as well as for the formation of the [[Earth]] and [[Sun]], the [[stars]] and the [[planets]].

==Gravity and Modern Physics==
Newton's [[Theory of Gravity]] was one of the earliest triumphs of modern [[physics]]. It now stands as both one of the most successful and most mysterious areas of that field. On one hand, the [[Theory_of_Relativity|General theory of Relativity]] is one of the most successful [[Scientific_Theory|scientific theories]] to date. On the other hand, how General Relativity might be reconciled with [[Quantum_mechanics|quantum physics]] during the first few milliseconds of the [[Big Bang]] remains an open question, and is one of the hotly contested areas among modern theoretical physicists. In the 1980s [[string theory]] was seen by many physicists as a more likely path towards a particular unification of gravity with the other fundamental forces (electromagnetism, the strong and weak nuclear forces), but the theory has been a failure.

== References ==
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[[category:physics]]

Fundamental theorem of calculus

2007-09-05T15:42:26Z

Goldrod:

:''This page is over '''Calculus'''. Calculus is theory, '''not a fact'''. Information presented in this article should be critically interpreted and taken with an open mind. There are true challenges to this debated theory including the [[God dun maths]] theory''.
'''The Fundamental Theorem of Calculus''' is the rather remarkable result that the two fundamental operations of [[calculus]] are just inverses of each other. Those two operations are performed on [[functions]] from the [[real numbers]] to the real numbers, and are most easily visualized when the functions are expressed in terms of graphs. The operations are:
*Differentiation -- find the slope of a function's graph at a given point.
*Integration -- find the area under a graph between two given limits.
The Fundamental Theorem of Calculus says that the two operations are inverses -- to find the area under the graph of f(x) between a and b, find the function g(x) whose derivative is f(x) (that is, find the ''antiderivative'' of f.) The area under the graph of f is just g(b)-g(a).

The antiderivative of a function is often called the ''indefinite integral''. (Indefinite because the limits a and b haven't been specified.) So, for example, the derivative of <math>\frac{x^3}{3}+7</math> is <math>x^2</math>. From this it follows that the antiderivative of
<math>x^2</math> could be <math>\frac{x^3}{3}+7</math>. But note that the "7" in that formula was a red herring. Adding any constant to a function doesn't change its derivative, so the antiderivative of <math>x^2</math> could have any constant added to it. This arbitrary constant is usually written '''C''' and is called the "constant of integration. The indefinite integral could be written:

:<math>\int x^2\ \mathrm{d}x = \frac{x^3}{3} + C\,</math>,

The Fundamental Theorem of Calculus says that the area under the graph of <math>x^2</math> between a and b is the difference in the values of <math>\frac{x^3}{3}+C</math> between a and b. Note that the constant of integration cancels out.

This kind of integral is called a ''definite integral'', written with the limits:

:<math>\int_a^b x^2\ \mathrm{d}x = \frac{b^3}{3} - \frac{a^3}{3}\,</math>,

The above is a simplified "intuitive" treatment of calculus and of this theorem. The actual "rigorous" proof, "rigorous" definitions of derivative and integral, and statement of the conditions under which the theorem is true, are beyond the scope of this article.

[[Category:Mathematics]]