All Questions
15 questions
1
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2
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105
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Why must a constraint force be normal?
If we impose that a particle follows a holonomic constraint, so that it always remains on a surface defined by some function $f(x_1,x_2,x_3)=0$ with $f:\mathbb{R^3}\rightarrow\mathbb{R}$, we get a ...
- 131
-1
votes
1
answer
51
views
Proving the relation $\frac 1 2 \left[\nabla^2,r \right] = \frac 1 r + \frac \partial {\partial r}$ (quantum mechanics exercise) [closed]
I'm trying to prove this relation in my quantum mechanics exercise book
$$\frac 1 2 \left[\nabla^2,r \right] = \frac 1 r + \frac \partial {\partial r}.$$
Here's my attempt:
Expand the Laplacian ...
- 301
-2
votes
1
answer
3k
views
What is the General formula of gradient of $r^n$? [closed]
so, the question is that r is the separation vector from a fixed point $(x',y',z')$ to the point $(x,y,z)$ and let $r$ be its length.
the answer to the question of what is the general formula of $$\...
- 17
1
vote
2
answers
159
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One object moves along the cycloid at a constant rate, how about its acceleration? [closed]
We know that the parametric equation:
$$x=R(\theta+\sin(\theta))$$
$$y=-R(1+\cos(\theta))$$
and the constant velocity $c$.
How do I prove that the acceleration of the object in the $y$ direction is ...
- 21
0
votes
1
answer
435
views
Find the distance travelled between $t=0$ and $t=5$ [closed]
The position vector of a particle is given as $\vec r = \frac43 t^{3/2}\hat i - \frac{1}{2} t^2\hat j + 2 \hat k$, $t$ is in seconds. Find the distance travelled between $t = 0$ and $t = 5$ seconds.
...
- 231
0
votes
1
answer
204
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Can you apply product rule to arg of a bra-ket?
I found the following expression in a paper:
$$
\frac{d}{dt}\arg\langle\phi_+|\dot{\phi_-}\rangle
$$
where the $\arg$ term is the argument of the complex number given by inner product between two ...
- 591
0
votes
2
answers
84
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Acceleration in a non-inertial reference frome - derevation
The general velocity equation for a point B in on body rotating and translating about point A with respect to the inertial reference frame say 'xyzo' can be expressed as,
$\vec{r_{B/o}} = \vec{r_{A/o}...
- 17
-1
votes
1
answer
149
views
Basic vector calculus: Show that $\nabla \vec{r} = \vec{1}$ [closed]
Show that $\nabla \vec{r} = \vec{1}$
My instructor in my E & M class put the $r$ and $1$ in bold. I am not sure what a bold one means. From my work I get $1ii + 1jj + 1zz$.
- 119
-1
votes
2
answers
273
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How can I show that the acceleration vector for uniform circular motion undergoes uniform rotation?
Does it suffice to show that the dot product between the acceleration vector and the derivative of the acceleration vector = 0?
- 39
0
votes
1
answer
482
views
Partial Derivative of a scalar (absolute distance) with respect to its position vector
Imagine we want to take the partial derivative of a quantity, we will call it $\rho_i = f(F(r_{ij}))$ with respect to a particle's position vector, $\vec{r}_k$.
In mathematical terms, this would be ...
- 15
0
votes
1
answer
274
views
Kinetic energy derivation: Why is $\frac{d \mathbf v}{dt} \cdot \mathbf v= \frac 12 \frac{d}{dt}(v^2)~?$
In Goldstein's Classical Mechanics 3rd edition, page 3, the Kinetic energy is derived by considering the work done on a particle by an external force $\mathbf F$ from point $1$ to point $2$ $$W_{12}=\...
user138458
-1
votes
3
answers
69
views
Vector question, differentials, Electromagnetism
I was reading this demonstration of electric potential in my book:
Let $q$ be a point charge at point $P$
The Electric field created at point $M$ by $q$ is :
$$\vec{E}(M) = \...
- 685
0
votes
1
answer
268
views
Gradient of two-particle system
I'm working on problem 5.1a from Griffiths Intro to QM and given that:
$$\mathbf R \equiv \frac{m_1\mathbf{r_1} + m_2 \bf r_2}{m_1+m_2}$$
and $\bf r \equiv \bf r_1 - \bf r_2$ I need to show that,
$$\...
- 207
0
votes
1
answer
68
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The vector r points from $P'(x',y',z')$ to $P(x,y,z)$ [closed]
For some reason this question is giving me a hard time :(
The vector $r$ points from $P'(x',y',z')$ to $P(x,y,z)$.
(a) Show that if $P$ is fixed and $P'$ is allowed to move, then $\nabla'(\frac{1}{r}...
- 817
1
vote
4
answers
9k
views
Dot product of vector and its derivative with respect to time? How does $L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$? [closed]
How does:
$$L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$$
where L is a vector (I dunno how to make it bold in the equation).
How do they reach to this right hand side equation?
And what is ...
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