# Questions tagged [approximations]

The tag has no usage guidance.

445 questions
Filter by
Sorted by
Tagged with
90 views

### “Newtonian limit” property of special relativity

Books say that special relativity is indistinguishable from Newtonian mechanics when the speed of the primed frame ($v$) is small compared to the speed of light ($c$). This is what I mean by the "...
138 views

### problem with Sudden Approximation in quantum mechanics

If the Hamiltonian of a system changes abruptly (over a very short time interval) from one form to another, we would expect the wave function not to change much, yet its expansion in terms of the ...
141 views

722 views

### Understanding multipole expansion in classical electrodynamics

I am trying to better understand what the multipole expansion means from a phyiscal point of view. Although mathematically, one may say it is just another form of a series expansion, in this case, the ...
131 views

### Better approximations with two sticks

How approximation ought to be done always confuses me. Considering this problem in a textbook: Two massless sticks of length $2r$, each with a mass $m$ fixed at its middle, are hinged at an end. ...
193 views

469 views

### Neglecting second order differentials

I am currently doing some Lorentz invariance exercises considering infinitesimal Lorentz transformations, and have been told to neglect second order differentials. It's not the first time I have come ...
612 views

447 views

### Singularity in Newton's gravitational law [duplicate]

If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite? May someone please clarify it to me?
4k views

### Why is the elemental volume of a sphere equal to $4 \pi r^2dr$?

I was doing this question on calculating the electric field at a certain point in a sphere (length $r$ away from the centre), where the charge density is given by an equation. When I checked the ...
411 views

### How to derive a formula for the period of a simple pendulum? [duplicate]

The following formula is given in our lab manual: $$T = 2 \pi \sqrt{\frac{L}{g}} \left( 1 + \frac{1}{4}\sin^2 \frac{\theta}{2} + \frac{9}{64}\sin^4 \frac{\theta}{2}+\cdots \right)$$ for the period ...
114 views

### What are point objects?

I can't seem to get the idea of point mass into my head. Why are equations of physics applicable on only point masses and should be altered while dealing with object that has a collection of points? ...
2k views

### Why can we assume, when dealing with tension, that the mass of a rope is $0$ but still assume that there are forces on it?

I started studying tension and I can't understand the following concept: If I have two objects $A,B$ collegated by a rope, where $A$ applies a certain force $\vec{F}$ on it, I would have that the ...
228 views

### Derivation of velocities in the Coriolis force

In Fitzpatrick's Newtonian Dynamics book on the Coriolis force, he states \begin{align} v_{x'}&\simeq V_0\cos\theta-2\Omega t V_0\sin\lambda~\sin\theta \tag{433}\\ v_{y'}&\simeq-V_0\sin\...
146 views

86 views

### Why does quantum mechanics become unnecessary at sufficiently high temperatures?

In my statistical mechanics intro class, we are taught that at sufficiently high temperatures, the quantum treatment of things becomes unnecessary. Why is this? Can this be shown using certain ...
105 views

### Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
196 views

### Why do materials obey Hooke's law? [duplicate]

Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that when materials are compressed or extended under force, their atoms become closer or further apart; ...
1k views

### Tidal force formula

My book explains what happens if we measure the difference in gravitational force by displacing a test mass by $\Delta r\ll r$. They give the following formula: $$\Delta F=\frac{2GMm\Delta r}{r^3}.$$...
152 views

### Calculating size of opening of a Decanter in order to project 5 gallons of water per second 20 feet in the air vertically?

This question is attempting to determine the size of the opening of a Decanter of Endless Water for our gaming group. We are wanting to hook it up to some impromptu Jerry-rigged technology as either a ...
92 views

### In geometrical optics, how can we say that rays coming from a distant object are parallel to one another?

If two rays are not parallel in the start, how can they become parallel at the instant when they strike the lens of a telescope? If they don't become parallel, why do we consider them to be, in the ...
5k views

### 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 ...
391 views

115 views

### Changing Summation to Integral

This is the text from Reif Statistical mechanics. In the screenshot he changes the summation to integral(Eq. 1.5.17) by saying that they are approximately continuous values. However, I don't see how. ...
As time increases, the amplitude and frequency of the GW signal also increase. But after using the stationary phase approximation, the signal is proportional to ${1/f^{7/6}}$, where $f$ is the GW ...