All Questions
4
questions
-1
votes
1
answer
116
views
How does one prove that the conservative force $\vec{F}$ is equal to the negative gradient of the potential $V$?
I have a grasp of the gradient theorem, and I understand that if we let $\phi$ be a function such that $\vec{F}=\nabla \phi$, and $V(\vec{x})$ be the potential at $\vec{x}$, then
$$-\int _C\vec{F}d\...
- 379
1
vote
1
answer
146
views
How to choose the sign of the differential?
I know this is a very simple question, and I have searched it too. How to avoid incorrect symbols in calculation results.I don’t understand how to choose the sign of $ds$.
An object moves from a to b,...
- 35
0
votes
1
answer
268
views
Integral limits when calculating the work
If I integrate
$$dW= \vec{ F} \cdot d\vec{\ell}$$
which are the limits?
In
$$\int\limits_{W_{inf}}^{W_{sup}}dW= \int\limits_{\vec{\ell}_{1}}^{\vec{\ell}_{2}} \vec{ F} \cdot d\vec{\ell}$$
it is ...
- 165
2
votes
2
answers
2k
views
Definition of torque for a continuous body
I am working on basic physics definitions. Given a particle at position $r$ (in some coorinate reference system) upon which acts a force $F$, the $torque$ $\tau$ is defined by
\begin{equation}
\tau:=r\...
- 279