Questions tagged [calculus]

Calculus is the branch of mathematics which deals with the study of rate of change of quantities. This is usually divided into differential calculus and integral calculus which are concerned with derivatives and integrals respectively. DO NOT USE THIS TAG just because your question makes use of calculus.

Filter by
Sorted by
Tagged with
0 votes
1 answer
19 views

What is displacement time graph for this object which is in $xy$ plane going in sine wave like path from A to B. Also can velocity constant in path?

The path is from A to B in sine wave curve while the displacement is straight line.So how displacement is calculated for graph purpose here
user avatar
2 votes
0 answers
32 views

Solving for the radius of a sphere as a function of time

I have tried to realistically model the famous game Agar.io, which can described as the following: A sphere of initial mass $m_0$ expels part of its mass at a given rate ($\frac{dm_l}{dt}$) for thrust ...
user avatar
  • 290
0 votes
0 answers
12 views

What is the irradiance of an extended source?

For example, what is the irradiance at a certain A = 2m^2 surface from a P = 10W tube lamp with significant radius and length - say, r = 15mm L = 100mm - measured at a small distance - say, d = 2m? ...
user avatar
  • 1
10 votes
7 answers
1k views

What is the instant velocity? [duplicate]

The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
user avatar
  • 117
2 votes
0 answers
34 views

The Partition Function of $0$-Dimensional $\phi^{4}$ Theory

My question is related with this question. Several years ago, I posted an answer to the question, and the author of the reference removed the link permanently, now I have no clue what's going on. In ...
user avatar
0 votes
1 answer
30 views

Doubt in derivation of bending of beam, It's about derivatives and intergration

Radius of curvature of the beam in above picture is given as: $$ \frac{1}{R} = \frac{d^2 y}{dx^2}$$ Please help me two points used as steps of a derivation in my book: How was the radius of ...
user avatar
  • 3
1 vote
1 answer
79 views

What is the origin of these log terms in dimensional regularization?

The following limit is implied on page 250 of Peskin and Schroeder: $$\Gamma\left(2-\frac d2\right)\left(\frac 1 \Delta\right)^{2-\frac d2} \xrightarrow{d\rightarrow 4} \frac 2\epsilon - \log \Delta -\...
user avatar
  • 441
0 votes
5 answers
101 views

Why do kinematic equations only work with constant acceleration?

People say that the equations are derived assuming a constant acceleration. I just don't see how this is the case. (I am new to calculus.)
user avatar
  • 71
0 votes
0 answers
26 views

Minimum seperation of moving objects doubt

Let there be $2$ objects $P_1$(initial velocity $u$ $ms^{-1}$ & acceleration $a$ $ms^{-2}$) & $P_2$ (initial velocity $U$ $ms^{-1}$ & acceleration $A$ $ms^{-2}$) initially separated by ...
user avatar
0 votes
1 answer
38 views

Time derivative of unit velocity vector?

Let's say I have some parametric curve describing the evolution of a particle $\mathbf{r}(t)$. The velocity is $\mathbf{v}(t) = d\mathbf{r}/dt$ of course. I am trying to understand what the expression ...
user avatar
0 votes
0 answers
30 views

How to evaluate a non-banal derivate?

I need to evaluate the following derivate: $$\frac{dF}{d\Psi} = \frac{d}{d\Psi}\left[\beta\Delta\Psi+\alpha\left|\Psi\right|^2\Psi+\mu\Psi-i\vec{v}\cdot\bar{\nabla}\Psi\right]$$ where $\Psi$ is a ...
user avatar
0 votes
1 answer
18 views

2D rotation dynamics/control systems as a complex number

I have a dynamic system (it's a rocket in a 2D plane), that I'd like to model the orientation of using complex numbers to remove the need for trig functions in my ode. I'm having trouble defining the ...
user avatar
  • 1
1 vote
0 answers
17 views

Force to Inflate a ball underwater [closed]

How much force is required to fully inflate (with air) a beach ball that is 6 feet in diameter at depths of 200 feet underwater?
user avatar
0 votes
1 answer
97 views

Trying to derive newtonian potential for Schwarzschild interior metric [closed]

I am using the book "A first course in general relativity" by Bernard Schutz. On page 267 he derives equation 10.54 but leaves out some steps that I am trying to do myself. The following is ...
user avatar
  • 788
1 vote
1 answer
40 views

On taking the gradient of a compressible fluid potential

In literature I read: $$\tag{1} \mathbf{q}=(Nd^2)(\rho/\mu)[\mathbf{g}-(1/\rho) \nabla p]=\sigma \mathbf{E}$$ which is valid for liquid generally, and for gases at pressures higher than about 20 ...
user avatar
  • 1,245
0 votes
0 answers
14 views

Using Variation of Energy for a Dielectric to define the Electric Field

I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
user avatar
1 vote
2 answers
49 views

Confused about the solution to the pendulum differential equation

So I’ve learned how to derive the exact solution to the pendulum differential equation (in respect to its period), $\ddot{\theta} + \frac{g}{l}\sin\theta=0$, where $g$ is gravitational acceleration ...
user avatar
  • 113
0 votes
2 answers
46 views

On a minima problem in optics

I have trodding through a calculus textbook, more specifically — through a chapter on the methods of obtaining the extrema of functions using derivatives, including certain problems in optics (Fermat’...
user avatar
3 votes
1 answer
127 views

What is the equation for the mass of an evaporating black hole over time?

We predict that black holes will lose mass over time due to Hawking radiation. I want to find an equation for the mass over time $M(t)$ of a black hole with initial mass $M_0$ in an otherwise empty ...
user avatar
  • 285
-1 votes
1 answer
66 views

Why can you remove constant when taking the derivative? [closed]

If the derivative of a constant is 0, why can we just remove this constant when differentiating? eg. If d/dx(3x^2+5x+1), can we write this as d/dx(3x^2)+d/dx(5x)+d/dx(1). If so, what allows us to do ...
user avatar
2 votes
1 answer
59 views

Does the expression "$𝑑𝑠^2$..." mean the same thing as "$\Delta 𝑠^2$... "?

I reviewed this question but sometimes I'm unsure about delta versus differential notation. Does the expression "$ds^2=-c^2dt^2+a^2(t)[dr^2 + S_k^2(r)d\Omega^2 ]$" mean the same thing as &...
user avatar
0 votes
1 answer
35 views

Why do we use cubic fluid elements when deriving fluid equations?

Recently I've been delving into fluid dynamics but is frequently troubled by a conceptual issue that I could never get my head around with. To derive fluid equations, we have to separate fluid into ...
user avatar
0 votes
1 answer
49 views

Does it actually make sense to talk about velocity of the point of contact of a wheel rolling without slipping?

I was reading this answer where I saw the following gif: We can see that when a point becomes point of contact (i.e: touching the ground), the curve of it's motion has a cusp. To my knowledge, a cusp ...
user avatar
14 votes
3 answers
3k views

Why does solving the differential equation for circular motion lead to an illogical result?

In uniform circular motion, acceleration is expressed by the equation $$a = \frac{v^2}{r}. $$ But this is a differential equation and solving it gets the result $$v = -\frac{r}{c+t}.$$ This doesn’t ...
user avatar
  • 143
-2 votes
1 answer
72 views

Function must be discontinuous over $r=0$ due to physical impossibility [closed]

In this question it is asked what the upper-bound of the ratio of a solid object's surface area can be visible through direct, unaided observation. The accepted answer says that there is no such upper-...
user avatar
0 votes
0 answers
26 views

How do the cusp conditions for helium atom translate from $(r_1, r_2, r_{12}) \to (r_1, r_2, \Theta)$?

While trying to make a Helium atom ground-state solver, I encountered the Cusp conditions initially derived by Kato et al. and then generalised by C. C. J. Roothaan and A. W. Weiss $$\lim_{r_{i} \to 0}...
user avatar
0 votes
1 answer
54 views

How do I take the gradient of the position operator?

I have a function $$g(\hat{\vec{x}}) = e^{-(\hat{\vec{x}} - \vec{r})^2 / 2r_c^2}$$ Here, $\hat{\vec{x}}$ is the position operator, $r_c$ is parameter and $\vec{r}$ denotes a classical position. I want ...
user avatar
3 votes
3 answers
183 views

How do you find the final velocity when acceleration is changing between two values over some distance? [duplicate]

How do you calculate a final velocity of an object when given its initial velocity and the object is accelerating between an initial and final acceleration over some given distance?
user avatar
  • 153
3 votes
7 answers
156 views

What exactly is rest?

Consider a position-time graph for a particle's motion, where the y-axis is position and the x-axis is time (in seconds). Now, consider the question: At what point in time is the particle at rest? ...
user avatar
2 votes
3 answers
171 views

Electric field at a very distant point of an wire from generic point in space

I calculated the electric field at a generic point in the space $P(a,b,c)$ due to an wire with charge density $\lambda$, constant and positive, length $L$, with axis in $z$ direction and origin in the ...
user avatar
0 votes
1 answer
47 views

How is this possible (electric field integral)?

In the electric field subject, $dq$ is ok to integral. How is this possible? $Q$ is not even changing variable. Can you explain its math? $$E=k\int \frac{dq}{r^2}.$$
user avatar
0 votes
2 answers
70 views

Finding angular frequency via integration of Newton's Second Law for a physical pendulum

For context: I am a student enrolled in AP Physics C with prior knowledge from AP Calculus AB and AP Physics 1. We just collected data for a lab to determine an experimental value for g. The setup ...
user avatar
0 votes
1 answer
56 views

Lagrange Multipliers

In this Lagrangian (from the paper: https://arxiv.org/abs/1302.0192 - page 4), $\eta, \mu, \nu, \& \lambda$ are lagrange multipliers. My question is: why do they include $\nu$ and $\lambda$ ...
user avatar
  • 67
1 vote
1 answer
72 views

Meaning of big $O$ notation with 2 values separated by a comma

I'm reading Classical Electrodynamics 3e by Jackson. In section 1.7 he performs a proof of the Poisson equation in the context of the electric potential. Near the end of the proof, he writes $$ \...
user avatar
  • 135
0 votes
0 answers
41 views

Why while solving some specific problems like this we need the second-order variation like this one?

Consider a string which is fixed at both ends and we are giving it a small amplitude by tauting it and moving to and from. If someone wants to derive the wave equation of the string, they would first ...
user avatar
  • 485
0 votes
2 answers
67 views

Intuition behind a line integral over a vector field

I have seen answers to this question on this site already, though I still do not understand what line integrals and there results represent and would appreciate an oversimplified description. I have ...
user avatar
1 vote
0 answers
67 views

Convergence of an oscillatory integral to real number

I have a physical model, where the long-time behavior of the system can be described by $$C(t)=\frac{1}{2\pi}\int_{-\pi}^\pi\mathrm{d}k\,\mathrm{e}^{-t\omega(k)}$$ with $\omega(k)\geq0$ and $\omega(t)\...
user avatar
0 votes
1 answer
42 views

Using a stress-energy tensor in linearized Einstein equations

I am using a known stress-energy tensor to try to find $h_{\mu\nu}$, the small deviations from flat space in the linearized Einstein formalism. In harmonic gauge, $$ \square h_{\mu\nu}=-16\pi GT_{\mu\...
user avatar
0 votes
3 answers
118 views

Limit of $d\rightarrow 4$ of a function in Peskin & Schroeder

In Peskin & Schroeder section 12.1 equation 12.15 we compute the function $$ \frac{-3\lambda^2}{(4\pi)^{d/2} \Gamma(\frac{d}{2})}\frac{(1-b^{d-4})}{d-4}\Lambda^{d-4} $$ Now when we take the limit $...
user avatar
1 vote
1 answer
70 views

Acceleration as a function of displacement

I am given a question such that a 0.280kg object has a displacement (in meters) of $x=5t^3-8t^2-30t$. I need to find the average net power input from the interval of $t=2.0s$ to $t=4.0s$. I know the ...
user avatar
  • 115
0 votes
2 answers
153 views

Why isn't tangential acceleration just always 0?

This is probably a very stupid question but I can't help me. Tangential acceleration is $\vec{a_t}=\frac{dv}{dt}\frac{\vec{v}}{v}=\frac{\vec{v} \cdot \vec{a}}{v} \frac{\vec{v}}{v}$. Since $\vec{a}$ is ...
user avatar
  • 15
-1 votes
1 answer
65 views

How did the differentiation with respect to the vectors done here?

A system of particles interacting through a two-body potential $u(\vec r_j-\vec r_i) $. Assuming the interparticle potential to be central and denoting it by the symbol $u(r) $, where $r=|\vec r_j-\...
user avatar
2 votes
1 answer
30 views

How to use a piecewise acceleration function to get a position function?

This should be a relatively easy problem but I think I am missing something somewhere. This problem consists of a object that is being thrown into the air at $t = 4s$ at a velocity $v_0$ here is my ...
user avatar
0 votes
0 answers
34 views

2D Fourier transform of 3D Yukawa potential

I am basically trying to take the 2D Fourier transform of the 3D Yukawa potential. Hence, I have the following function \begin{equation} f(\textbf{r}-\textbf{r}')=\frac{e^{-a|\textbf{r}-\textbf{r}'|}}{...
user avatar
  • 117
0 votes
1 answer
42 views

How to determine terminal velocity with speed reduction percentage and constant acceleration?

So I'm developing this game with physics. Every frame, the body accelerates at $+4\,\mathrm{m/s^2}$. However, every frame, the body also sets its velocity to 90% of its original value, basically the ...
user avatar
0 votes
1 answer
64 views

Find that $d\left(\frac{\mu}{T}\right)=ud\left(\frac{1}{T}\right)+vd\left(\frac{P}{T}\right)$

Find that $d\left(\frac{\mu}{T}\right)=ud\left(\frac{1}{T}\right)+vd\left(\frac{P}{T}\right)$ $$U=TS-PV+\mu N\tag{1}\label{1}$$ $$dU=TdS-PdV+\mu d N \tag{2}\label{2}$$ From equation \eqref{1} $$dU=...
user avatar
  • 7
-2 votes
1 answer
108 views

A ball is dropped from a height of 1m above the ground.What will be the instantaneous speed of the ball when it is exactly at 1/2 mark? [closed]

I saw this question in this video Instantaneous speed (differentiation) by Don't Memorize In the video, the instantaneous speed of the ball is given as 100cm/sec which is equal to 1m/sec but when I ...
user avatar
0 votes
0 answers
11 views

Issue with work vs force for calculating spring constant [duplicate]

Lets say I have a spring with spring constant k. I put a 10kg weight on the spring and it compresses the spring one meter before stopping. We know that at this point the downwards force is equal to ...
user avatar
1 vote
1 answer
34 views

Which of the following two inequalities related to kinematics is wrong with reason?

Problem was this: For a particle moving in space with velocity $\vec{V}$, which of the following is incorrect? (A) $\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \geqslant \...
user avatar
  • 485
1 vote
2 answers
86 views

Derivation of $\mathrm{d}\vec{S} = \mathrm{d}r \hat{r} + r \mathrm{d}\theta \hat{\theta}$

In polar coordinates, I know $$\mathrm{d}x = \cos\theta\, \mathrm{d}r - r \sin\theta \,\mathrm{d}\theta,$$ and $$\mathrm{d}y = \sin\theta \,\mathrm{d}r + r \cos\theta\, \mathrm{d}\theta,$$ thus I ...
user avatar
  • 11

1
2 3 4 5
17