New answers tagged calculus
0
votes
Why must the total time derivative only be a linear function of velocity?
It comes down to how the differentiation works. The function I mentioned, $f(q, t)=q^2$ would indeed be a linear function once differentiated:
$$\frac{d}{dt}(q^2)=\frac{d}{dt}(q\cdot q)$$
Which, when ...
0
votes
Why must the total time derivative only be a linear function of velocity?
The Taylor expansion is:
$f(x+\delta)=f(x)+f'(x)\delta+...$
Here $x=v^2$, and you know that
$v^2+\delta=(\vec{v}+\vec{\epsilon})^2=v^2+2\vec{v}.\vec{\epsilon}+\epsilon^2$
thus,
$\delta=2\vec{v}.\vec{\...
- 1,809
1
vote
Why are independent variables treated differently in kinetic energy calculations across problems?
you start always with the position vector to the masses .
Case I
$$\vec P_m=\begin{bmatrix}
X \\
Y \\
\end{bmatrix}=\left[ \begin {array}{c} \left( l+x \right) \sin \left( \phi
\right) \\ - \...
- 12.9k
1
vote
Limits of the integral for the calculation of work
This response is specifically to this section of your question:
I know that for potential energy the above statement is correct, one can choose the reference (zero) value as one wishes. But, for ...
- 22.6k
1
vote
Accepted
Continuity of Electric Potential in the Vicinity of a Charged soap bubble
The problem with your solution
The problem is that your electric potential is wrong. The way you calculated it is vague, and to get the correct expression we should be more careful.
If you have a ...
- 3,377
3
votes
Limits of the integral for the calculation of work
I think this is one of the cases when we apply a rule beyond its applicable limits.You cannot define boundary conditions to quantities which describe energy transfer because they dont physicaly make ...
- 372
5
votes
Limits of the integral for the calculation of work
One way to think of an expression like $dW = F dx$ is that it is a physicist shorthand for a differential equation. In this case, the differential equation for $W$ is a first-order ODE
$$
\frac{dW}{dx}...
- 55.4k
0
votes
Limits of the integral for the calculation of work
When you integrate a function, the limits of integration always have the units of the differential. We usually integrate from a starting unit to a generic unit. In that case, you would integrate:
$$
\...
- 1
2
votes
Accepted
Connection between gravitational potential function and Gaussian distribution function in 3 dimensions
Since no one provided an answer, I'll do it. But I don't know what user_1_1_1's mathematical background is, so I will try to give links to every keyword I am using.
The "probability amplitude&...
- 2,803
Top 50 recent answers are included