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Are some laws in physics really as simple as they seem?

For example, is $F = ma$ really an exact formula, or is it an approximation? I know a lot of formula's come from taking the first few terms of a Taylor expansion, so I was wondering if the simple ...
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Why Earth is considered to be an inertial frame? [duplicate]

Earth rotates about its axis and also revolves around the Sun at the same time. So why Earth is considered as an inertial frame in Newtonian Physics. So technically, I'm effectively asking why the ...
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The angle of a rifle to hit a target (How to make approximations to find numerical answers) [closed]

The specific question is this: A target appears at a distance of 1250m with the centre of the target 1.2m above ground level. If the sniper was firing from the prone position, the tip of the ...
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Multiple Definition For Gravitational Potential Energy?

This may just be a simple Misconception Question, here goes: Definition for Gravitational Potential Energy: The work done by gravity to pull an object to the ground. ...
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In perturbation theory, how do I determine the order of an approximation?

The title says it all: I'm confused about the various approximations and their orders. In time-independent perturbation everything is quite explicit and obvious, but, for example, how would it be with ...
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Systems with elements having size which tends to zero

[Question] If I have an element whose size(as in physical dimensions) tend to 0 but is NOT 0 (very very very small). If I create a system from these elements based on (say) the fractal concept ...
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Is “approximative reduction” general knowledge to physicists?

I came across this concept called "approximative reduction", about which there are some papers, e.g. in this collection called Structure and Approximation in Physical Theories. Very briefly, it ...
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Fresnel diffraction approximation (parabolic waves)

The Huygens-Fresnel principle (Introduction to Fourier Optics, Goodman), $$U(x,y)=\frac{z}{i\lambda}\int_\Sigma U(\xi,\eta)\frac{e^{ikr}}{r}d\xi d\eta\,,$$ where $\cos \theta=\frac{z}{r}$, shows ...
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Why do some approximations give exact results?

The moment of inertia of a sphere of mass $M$ and radius $R$ can be calculated exactly (meaning, with certainty) using integrals. The formula we get is $\frac{2}{3}MR^2$. However, there's an other ...
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WKB boundary conditions [duplicate]

Technically, this is a math problem but I think it is better here than in the math stacks. Consider the differential equation $$y'' = (x^4 - E)y$$ The boundary ...
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What will be the equation of motion of driven pendulum for amplitudes beyond the small angle approximation?

When finding the period of a pendulum beyond the small angle approximation, we have to use integration for small interval of $\theta$ and elliptical integration. I was trying to apply this situation ...
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What's the difference between “numerical methods” & “mathematical analysis” as said by Feynman in his lectures?

While reading his lectures, I came to these lines: On the basis of Newton's second law of motion,which gives the relation between the acceleration of any body & the force acting on it,any ...
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Time Dependent Perturbation Theory Probabilities

(This is taken from Griffiths Quantum Mechanics): So suppose I have two states $\psi_{a}$ and $\psi_{b}$, and the particle starts out in the state $\psi_{a}$: $$c_{a}(0)=1\qquad c_{b}(0)=0.$$ To ...
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Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
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Why do we use the Coulomb potential for the hydrogen atom?

When solving the Schrodinger equation for the hydrogen atom, the Coulomb potential $V = \frac{e^2}{4 \pi \epsilon_0 r}$ is used. The Coulomb potential comes from classical electrodynamics, so why ...
In Griffith's Introduction to Quantum Mechanics p. 256, after figuring out $$E_n^2=\sum_{m\neq n} \frac{|\langle\psi_m^0|H'|\psi_n^0\rangle|^2}{E_n^0-E_m^0}$$ he says We could go on to calculate ...