# Questions tagged [approximations]

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### Why is the velocity in the horizontal direction constant for 2D projectile motion?

For 2D projectile motion, why is the velocity in the horizontal direction constant? I learned that we neglect air resistance, but why? And isn't there horizontal acceleration at the beginning when ...
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### Thick vs thin lens

What is the criteria to know whether a lens is thin or thick ? Suppose we have a lens of r1= 10 mm , r2= -10 mm and thickness is 5 mm. So, with this information what can we say about the lens whether ...
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### Perturbation to the flat space metric

from the geodesic equation for non-relativistic case where $$v_i\ll c$$ $$\frac{dx^i}{dt}\ll1,{\rm for }\ c =1$$ $$\frac{dx^i}{d\tau}\ll\frac{dt}{d\tau}$$using this the geodesic equation for proper ...
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### Coulomb's Law Question

The presentation of Coulomb's Law in various books occasionally has a note that the test charge, q2, must be small enough that it doesn"t alter the field of the first charge, q1. The same limitation ...
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### QM limit of QFT in Schwartz [duplicate]

In Matthew Schwartz's QFT text, he derives the Schrodinger Equation in the low-energy limit. I got lost on one of the steps. First he mentions that $$\Psi (x) = <x| \Psi>,\tag{2.83}$$ ...
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### How to reach $U = mgh$ Using Newton's Law of Universal Gravitation? [duplicate]

today i was curious about the potential energy, so, i started studying the Newton's Law of Universal Gravitation which its equation is \begin{eqnarray} U= -\frac{GMm}{r}.\end{eqnarray} Well, since i ...
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### Hooke's full unapproximated law

It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation. That is, the equation $F=-kx$ is only ...
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### Why is a particle non-relativistic when its kinetic energy is small compared to its rest energy?

For example, nucleons in nucleus are in motion with kinetic energies of 10 MeV. Their rest energies are about 1000 MeV. Kinetic energy of nucleons is small compared to rest energy. They are hence ...
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### How do we understand the results of $1/N$ or $\epsilon$ expansion beyond leading orders?

When we do $1/N$ expansions in, say, 2+1$D$ $O(N)$ models and try to extract all kinds of critical exponents from it, we get the following results for the scaling dimensions of various operators up to ...
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