All Questions
28 questions
0
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90
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Derivative of the product of a scalar function and a vector valued function
According to Berkeley Physics Course, Volume 1 Mechanics,
The time derivative of a vector valued function can be derived from the formula:
$$
\mathbf{r}(t) = r(t)\mathbf{\hat{r}}(t)
$$
where the ...
- 25
-1
votes
2
answers
80
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Problem with resources, Walter Lewin's third lecture
I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
-2
votes
3
answers
96
views
Why is it wrong to find centripetal acceleration using change of velocity over change of time?
This question asks to find the centripetal acceleration by giving the initial and final velocity over the change of time.
As shown, my book combined two rules to find the acceleration. I utterly ...
- 377
5
votes
5
answers
443
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Why does $\delta \vec{r} = \delta \vec{ \theta} \times \vec{r}$?
Hello fellow physicists,
I was trying to understand some behavior on rotating objects, specifically about the formula $\vec{v} = \vec{\omega} \times \vec{r}$.
The Book (Marion, J. B. (1965). Classical ...
2
votes
5
answers
348
views
Why does $\vec{r}\cdot\dot{\vec{r}}=r\dot{r}$?
Why is $$\vec{r}\cdot\dot{\vec{r}}=r\dot {r}$$ true? Before saying anything, I have seen the proofs using spherical coordinates for $$\dot{\vec {r}}= \dot{r}\vec{u_r}+r\dot{\theta}\vec{u_\theta}+r\sin\...
- 69
0
votes
1
answer
93
views
Schwartz "QFT and the Standard Model", eq. 15.59, derivative trick, deriving with a dot product
$$\frac{\partial }{\partial s}M(s)= \frac{p^{\mu}}{2s}\frac{\partial }{\partial p^{\mu}}M(s)\tag{15.59}$$
$$\ s=p^{2}$$
How does the derivative with respect to $s$ turn into the expression on the ...
- 149
1
vote
1
answer
170
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What does it mean to differentiate a scalar with respect to a vector?
I am reading the special relativity lecture notes that I got from a professor of mine. It says that the Lagrangian is
$$L = \frac{1}{2}m|\dot{\boldsymbol{x}}|^2 - V(\boldsymbol{x}) \tag{1}$$
The notes ...
- 1,254
1
vote
3
answers
233
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Problem with the constant magnitude of vectors if the change in the same vector is perpendicular to it [duplicate]
Note: I am merely a highschool student attempting to self-study Classical Mechanics, some of the assumptions I make are perhaps wrong, so please bear with me. Thank you.
This while can be condensed ...
0
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2
answers
414
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Why does tangential acceleration become 0 when the velocity is max? [closed]
I know that tangential acceleration equal to zero when the circular motion is uniform, but why is it equal to zero, when the velocity is max or min? Because there is no relation between the value of ...
- 11
0
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1
answer
43
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Are terms tangential acceleration and normal acceleration only used for instantaneous velocity?
Are terms tangential acceleration and normal acceleration only used
for instantaneous velocity?
- 23
-2
votes
1
answer
3k
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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 $$\...
- 17
0
votes
1
answer
39
views
Spherical and Cartesian forms of divergence [closed]
Suppose the electric field found in some region is $$\overrightarrow{E} = ar^3\vec{e}_r$$ in coordinates
spherical (a is a constant). What is the charge density?
So, using the spherical form of ...
1
vote
1
answer
94
views
Simple difference between module of velocity and time derivative of module of position [duplicate]
What is the conceptually difference between the two:
$$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
- 189
0
votes
2
answers
353
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 ...
- 15
0
votes
1
answer
129
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Why intuitively is the tangent vector the derivative of velocity of position with respect to their modulus?
When trying to find the tangential velocity, many textbooks define the tangent direction as one of the following:
or
Intuitively, why is the tangent vector the derivative of the position with ...
- 849
1
vote
2
answers
319
views
What is the time derivative of the linear velocity vector $\vec{v}\,(t)$?
If $\vec{v}\,(t)$ denotes linear velocity, we can then write $\vec{v}\,(t)$ as $|v(t)|\hat{v}$. My question is what is $\displaystyle\frac{d\vec{v}\,(t)}{dt}?$
The answer I have seen to this question ...
- 39
0
votes
1
answer
435
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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.
...
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-4
votes
1
answer
71
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Given that $m \dot v \cdot v = 0$ , how is it equal to $m \frac{d}{dt} (v \cdot v)/2$? [closed]
While studying about scalar triple product in vector algebra, I stumbled upon the following question with the solution.
I want know how is $m \dot v \cdot v $ = $m \frac{d}{dt} (v \cdot v)/2$?
- 1
2
votes
1
answer
292
views
Is the relation "slope=velocity" mathematically valid?
$\text{Slope= tan(angle with respect to positive X-axis)= scalar output}$
$\text{velocity= a vector }$
Source: Hugh D Young_ Roger A Freedman - University Physics with Modern Physics In SI Units (...
- 439
0
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1
answer
225
views
The time derivative of a vector not defined in terms of the time variable $t$
Recently I got a question where I needed to determine the time derivative of a position vector. However, the vector didn’t have the variable $t$ but instead had $x$, $y$, and $z$ as its terms, so I ...
- 193
1
vote
6
answers
713
views
Why does differentiating a scalar give a vector? [closed]
I was wondering why $F=-\frac{dU}{dr}$ would give me a vector quantity when a scalar quantity is differentiated. There are similar pre-existing queries but I think this issue has yet to be properly ...
1
vote
1
answer
50
views
Path Coordinates: direction problem (doubt) in derivative of tangential vector
Why is the direction of derivative of tangential vector perpendicular to the direction of the tangential vector?
- 29
0
votes
1
answer
509
views
Divergence of a vector multiplied by dot product [closed]
If I am correct, then
$\operatorname{div} [(\vec A\cdot \vec B)\vec C] = (\vec A \cdot \vec B) \operatorname{div} \vec C + \vec C \cdot \nabla (\vec A\cdot\vec B)= (\vec A \cdot \vec B) \operatorname{...
- 113
2
votes
1
answer
278
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Dot product in cylidrical coordinates
I'm given the vector:
$$\vec{V}{(r,θ,z)}=\frac{1}{r}\hat{e_r} + (r\cosθ)\hat{e_θ}+\frac{z^2}{r^2}\hat{e_z}$$
I want the scalar product ${\vec{\nabla}}\cdot{\vec{V}}$
We know that in cylindrical ...
- 111
4
votes
2
answers
5k
views
How is dot or cross product possible using the del operator?
Yesterday in class my teacher told me that the del operator has a direction but no value of its own (as its an operator). So it can't be called exactly a vector. But in vector calculus we see that div ...
- 1,432
-1
votes
1
answer
651
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What is difference between $d\vec{l}$ and $\vec{dl}$? [closed]
What is difference between $d\vec{l}$ and $\vec{dl}$? $d$ means differential as usual.
- 15
4
votes
2
answers
861
views
Integration of tangential acceleration with respect to time
Here, by tangential acceleration, I mean the component of acceleration along the velocity vector.
What do you get when you integrate tangential acceleration with respect to time? What does the '$v$' ...
- 1,106
15
votes
3
answers
44k
views
Derive vector gradient in spherical coordinates from first principles
Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient.
I've derived the spherical unit vectors but now I don't understand how to transform ...
- 498