The Law of Conservation of Energy states: within a closed, isolated system, energy may change form, but the total amount of energy remains constant.

That is to say the sum of potential + kinetic energies = constant. Thus U + K = E.

The important part is that the TOTAL amount of energy remains CONSTANT.

Of course, a closed, isolated system is merely an abstraction, it doesn’t really exist. The earth is close, but there is still a small sum of external forces acting on it, as well as Mass that enters or leaves the system. (a closed system is one where Mass does not enter or leave the system, an isolated system is one where the net external forces acting on the system equals zero)

Now If and only if the change in energy is zero, THEN, initial energy equals final energy, that is to say E = E0

Some of you are sitting here thinking, where in the world is Joe going with this….you’ll find out soon.

A sphere is one of the most interesting shapes that exists in Geometry, All of you know that the Earth is in the shape of a sphere, but the reason why the earth doesn’t look like so from outerspace is because of the centrifugal force (that is really form of inertia) that “acts.” What you probably did NOT know is the fact that the sphere has the smallest Area/Volume ratio among any of the geometric shapes (3/r). So, again, why am I writing about this?

In Calculus, spherical coordinates are defined in terms of (ρ, θ, φ).

x = r cos θ sin φ

y = r sin θ sin φ

z = r cos φ

ρ^2 = x^2 + y^2 + z^2

Now, I know all of you remember quite nicely that a sinusoidal function is any function that behaves in such a matter y = a sin (b(x-h)) + k or y = a cos (b(x-h)) + k

So if we look at potential energy which as you should remember well by now is U = mgh and we let h be y we have potential energy as a function of a sinusoidal function.

and if I let Kinetic energy be zero (for the sake of defining it as so. to make math easier, I really don’t, but then I’d have to solve that messy sinusoidal function for the angle bx, (hell with it, i’ll do it for you bx = arcsin ((y-k)/a) + bh, and if you let b = 1 you get x = arcsin ((y-k)/a) + h.

Thus we end up with an energy function of such mg(a sin (b(x-h)) + k) + 1/2m(arcsin ((y-k)/a)+k))^2/t^2. Hideous right?

Well, I know all of you hear about this global warming BS.

Well, to put it simply, all that painful algebra and trig I just did was to show you that global warming is a bunch of BS.

Why? well, simply put, sinusoidal functions have ranges of what [-a, a]. That peaks and valleys should be expected. with Temperature (with Energy and Temperature being proportional). So any warming trend is natural due to the order of nature. Only God could of made something like this work out 🙂

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