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Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tags instead.

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14 views

What is th difference between resistance(R), inductance(Lu), capacitor (C) [on hold]

Give me defination of resistor, inductor and capacitor. With their units
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2answers
24 views

Need help understanding the derivation of Hydrostatic Equilibrium in a star

First and foremost I am sorry for this; in order to make my questions clear I must first upload the lecture notes from my institution $^\zeta$ for the derivation of Hydrostatic Equilibrium: $^\zeta$...
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0answers
28 views

Time gap between two cars

Lets say there is car A which average speed is 20 m/s and is ahead of car b by 200 meters while car b average speed is 21 m/s and both are on a racing track that is 1700 meters in length. what is time ...
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0answers
26 views

Prove angles of $(\vec r), (\vec v),(\vec a)$ are constant in this trajectory

Given the trajectory $$r(t)=[A\cos(\omega t),B\sin(\omega t+\alpha)]$$ Prove that the angles between $\vec{r}, \vec{v}, \vec{a}$ are constant. So the first idea is looking at the dot product and ...
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1answer
19 views

Find the height of a building given that it takes an object in freefall $1$ second to reach the ground from half the building's height

An object is dropped from a building of height $h\,\mathrm m$. The object falls half the total distance to the ground during the last $1.00\,\mathrm s$ of its fall. Find the height of the building. ...
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1answer
39 views

Identify type of equation or how to solve

I have a bit of a basic question as I can't recall exactly what it is. I have the function outlined below and I am unsure what type of equation it is or how to solve it, I just know that it requires a ...
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0answers
23 views

How to find Speed, Velocity, and Acceleration between two point $X_1, Y_1, Z_1$ and $X_2, Y_2, Z_2$

I have Excel sheet for $X, Y, Z$ coordinates. This data represent a locations for different points where hand moving during a 30fps video. I am trying to calculate Speed, Velocity, and Acceleration ...
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1answer
41 views

What do we call this operation(create a matrix from multiple vectors)? Unitary matrix?

Heisenberg used this operation to create a matrix from multiple vectors. $$x=\begin{pmatrix} \circ \\ \circ\\\circ\\\vdots \end{pmatrix}, y= \begin{pmatrix} \triangle\\ \triangle\\\triangle\\\...
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0answers
49 views

Is exterior calculus efficient for simple vector calculus problems?

Exterior calculus and invariant formulations are important and lead to many breakthroughs and great insights in physics and mathematics. But for daily vector calculus tasks, I still struggle to apply ...
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4answers
53 views

How can I find time in physics with a motion problem?

My problem is: A car slows down at $-5.00~\text{m}/\text{s}^2$ until it comes to a stop after travelling $15.0~\text{m}$. How much time did it take to stop? (unit $= s$) So this is how my school ...
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2answers
64 views

Calculate the constant acceleration needed for the discrete time trajectory to intersect a given target point

I have an object with an initial velocity in 2D space represented by a vector. I want to calculate a constant acceleration with a given magnitude required for the object to (potentially) change ...
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0answers
37 views

What is rank invariance?

I work in the area of soft matter and recently I have been reading a paper that talks about developing a new optimization algorithm for statistical physics problems. Turning statistical physics ...
1
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1answer
65 views

Fourier transform of product of Bessel functions

I need help finding the Fourier transform of the function $$ \rho(\vec{r}) = \alpha \delta_{\vec{r},0} \left(\lambda\lambda' J_1 (\beta |\vec{r}|)Y_1(\beta |\vec{r}|) - \pi^2 J_0 (\beta |\vec{r}|)Y_0(...
2
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1answer
55 views

Losing-mass oscillator - solving using Laplace transform

Statement of a problem Body of mass $M=m+m_0$ is moved out of balance ($x(0)=A$, $\dot{x}(0)=0$) and is subject to restoration force of magnitude $F = -kx$, where $x(t)$ describes position of body in ...
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2answers
42 views

General Equation for Acceleration

Question: A drum of radius R rolls down a slope without slipping. Its axis has acceleration a parallel to the slope. What is the drum’s angular acceleration α? To solve this question, I used the ...
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1answer
59 views

What does the floating point number $(1.2)$ down the bracket mean?

What does the 1.2 on the image mean? Thanks in advance.
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0answers
14 views

wave vector and its unit vector

$$ $$ My question is more related to physics. I know that for P-wave in an isotropic system the wave number is ${\left|q\right|}=\frac{\mathrm{\omega}}{\mathrm{vp}}$. What is $q$ (the wave vector) ...
2
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1answer
46 views

Showing the general solution reduces to $x(t)\approx \frac{F}{2mw^2_0\theta}\left(\sin(w_0t)-\sin(wt)\right)$

Consider the equation for a periodically forced, damped oscillator: $$m\ddot{x}+r_0\dot{x}+k_0x=F\sin(wt)$$ where $m, r_0, k_0$ are positive constants. Suppose now that $r_0=0$ and let $w_0=\sqrt{\...
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4answers
46 views

If your journey lasts 11 hours and 15 minutes what speed are you travelling at if you cover 90 miles? [closed]

I'm at a really loose end - I just can't seem to grab some fundamentals of Speed Distance Time. Can someone explain to me how they discover the answer to the following equipped with steps on how to ...
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2answers
26 views

Why is $\Delta (R_i^2)$ equal to $2R_i \Delta (R_i)$

So when deriving the equation for charge, I reached a point where $\frac{z\eta}{4\epsilon} \sum_{i=1}^N \frac{\Delta (R_i^2)}{(z^2+R_i^2)^\frac{3}{2}}$ But my teacher explains that $\Delta (R_i^2)$...
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1answer
25 views

Demonstrating the parallel axis theorem with double integrals

The collection of lines parallel to the y-axis have the form $x =a$. Let $I=I_y$ be the usual moment of inertia around the y-axis $$I=\iint_R x^2 \delta \, \mathrm dA$$ Let $\bar{I}$ be the ...
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1answer
45 views

The Metric Tensor Of A Cartesian Product

Hello I'm a physics student, not a math student, who is trying to understand how to write down the metric of a manifold which is constructed via a cartesian product of two other manifolds I know the ...
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0answers
52 views

Solving the derivative for a variable star's period and radius

I am trying to solve for $R$ as this is the radius of a RR Lyrae type of variable star from the formula: $$P-\frac{dP}{dT}=1.5R^{-1} \frac{dP}{dT}$$ $P$ is the star's brightness variability period and ...
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2answers
35 views

Clarification of the change in vector A

I understand that a change of the vector A can be the result of a rotation and a change in magnitude. (The perpendicular part and the parallel part) This can be represented by ΔA = ΔA(perpendicular) +...
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2answers
40 views

basic potential problem in mechanics

I am new to this field and I'm having trouble with this question where it asks me to calculate the potential from the basis of the origin. The question is: $\overrightarrow{F} = (0, -2y + 3y^2,0)$ ...
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0answers
76 views

Change of variables in a physics problem

Good day everyone, I am reading a paper and trying to reproduce some of the results in there. I do have to say this is a physics paper, so I am essentially sorry if the question I'm asking might seem ...
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1answer
22 views

Convert Area Density to Volumetric Mass Density

If the area density is 5.5kg/m², then what is its volumetric density in kg/m³?;) The thickness is 1/8 inch. I'm not getting the answer I'm being told is the correct answer and going nuts here;) ...
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1answer
53 views

The probability of photon collision

I was reading a textbook and I couldn't figure out something that seemed really obvious: Assume that the space is uniformly and randomly filled with stars, and the mean radial distance between the ...
4
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1answer
57 views

Are there interesting example of pseudo-Riemannian manifold other than spacetime manifold?

The 4 dimensional spacetime manifold is a typical example of pseudo-Riemannian manifold. Are there other mathematically or physically interesting example of it?
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1answer
33 views

Anti-derivative with velocity

a ball is thrown upward from the ground with speed of 96 ft/sec. Assuming that acceleration due to gravity is given by a(t)=-32 1-what does the velocity function? 2-what is the position function? ...
2
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1answer
39 views

Limit of arithmetic mean of series of measurements

Assume we have a series of measurements $x_i$ of, say, some physical quantity with (unknown) real value $x_r$. In a physics book I found the statement that, if we could exclude systematic errors in ...
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0answers
30 views

Naming matrices in a template pattern to solve multiple physics problems

On Lec 2 | MIT 18.085 Computational Science and Engineering I, Professor Strang introduces the stiffness matrix $A^\top C A$ such that in the vertical system of springs in the picture the following ...
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0answers
27 views

How to understand the Duhamel's principle

I have difficulty about the explanation of Duhamel's principle on my book. Here is what's written on my book: Take wave equation as an example. Consider the equation: \begin{cases} \frac{\partial^2u}{...
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1answer
53 views

My problem with the velocity of the object with position $z=t^2-t^3$.

(a) (b)Using first derivative test, $$\frac{dz}{dt}=0.$$ We get $t=2/3$. When $t=2/3$ object move $z=4/27$ units far from $z=0$. (c) Velocity at which object departed from $z=0,$ $$\frac{dz}{dt}|_{...
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2answers
40 views

How to calculate the mass of earth using triple integrals? [on hold]

How to calculate the mass of earth using triple integrals? The mass density of earth is $5.51 \,g/m^3$ The radius : $6353$ to $6384 \,km$ (average : $6371 \,km$) However, I don't even know ...
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2answers
59 views

Solution to ODE from Newton's Second Law

I have attempted to explore Newton's second law (F = ma) further into its many differential forms. I am not very familiar with differential equations and was searching for the steps and methods to ...
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0answers
139 views

What would you see inside a spherical mirror?

Image to build a huge spherical shell made of semitransparent glass, and to cover the internal part with a reflecting material. In such structure some light can enter, and an observer inside it (e....
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1answer
56 views

Solving the harmonic oscillator

so this is a bit of physics but the question is math related. For a mass hanging on a spring we get the following differential equation: $\ddot{z}+\frac{f}{m}\cdot z = \frac{m\cdot g + f\cdot z_0}{m}$...
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0answers
26 views

General solution of wave equation [duplicate]

A vector potential $A(x, t)$ satisfies the wave equation $\left(\Delta-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right) A(x, t)=0$. It is written in my physics textbook that the general solution ...
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2answers
41 views

Denominator doubled

Originally $a = 12 \space m/s$, then $r$ is doubled. Find the new value for $a$. $a = v^2/r$. If I am right, $v$ is originally $6$ which then turns to $36$ so if you divide it by $3$ it gives you $12$....
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2answers
28 views

Prove that $\sum_i \vec r_i \times \vec uF_i = (\sum_i \vec r_iF_i) \times \vec u$

Given an expression $$\sum_i \vec r_i \times \vec uF_i $$ where $\vec r_i$ are position vectors from the origin, $\vec u$ is a constant unit vector and $F_i$ are constants, it is true that$$\sum_i \...
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2answers
25 views

Achieving a step function with velocity

I need some help clarifying step functions. My question is can velocity step up? For example, is it possible for a body to accelerate from 0 to, say, 60 miles per hour in an infinitesimal or size-...
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2answers
75 views

Rigorous formulation of special relativity.

I want to understand the theory of special relativity and I am reading from Resnick's Introduction to Special Relativity. But I want to prove everything rigorously. $\newcommand{\R}{\mathbf R}$ $\...
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2answers
140 views

Mathematicians who research PDE and Analysis for fluid dynamics problems vs. Applied Mathematicians who conduct experiments, model and simulate

I'm close to the modeling, simulation, and experimental work in fluid dynamics, but I've been wondering about mathematicians that do analysis and PDEs: for example, what do physical quantities such as ...
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5answers
71 views

Solving second order ODE oscillator

I'm currently just taking my first ODE course and one of the questions is, A projectile of mass $m$ is fired from the origin at speed $v_0$ and angle $\theta$. It is attached to the origin by a ...
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2answers
56 views

Damped string motion partial differential equation

(i) A uniform stretched string of length $L$, mass per unit length $\rho$ and tension $T=\rho c^2$ is fixed at both ends. The motion of the string is resisted by the surrounding medium, the resistive ...
3
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2answers
46 views

Prove for the time derivative of a vector with constant magnitude

First of all, sorry for my bad English, I have several doubts about the geometric demonstration made by Kleppner for the derivative of a vector that has a constant magnitude, page 25, which is ...
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2answers
33 views

What model equations assumptions are made in order to claim that the behavior of solutions (trajectories) achieve some terminal behavior?

From maybe Calculus I or an undergrad physics course, one learns briefly about something called "terminal velocity", which seems to be accepted as true, although I've never looked for a proof of it. ...
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1answer
43 views

Amount of work required for pulling rope problem

50 m rope with 8 millimeters in diameter is dangling from an edge. density of rope =40 g/m. how much work to pull it up to edge? // I've seen different variations of this problem, but I am unsure of ...
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0answers
26 views

Norm minimization for mechanical blind force identification?

The differential equations steering motion in classical mechanics are very famous: $$\sum_i\frac{{\bf F}_i}{m}={\bf a} = \frac{d{\bf v}(t)}{dt} = \frac{d{\bf x}(t)^2}{dt^2}$$ Now to the question, ...