All Questions
15 questions
2
votes
1
answer
96
views
Why take the derivative of variables such as area, mass, and radius?
I'm taking a module on stars and the solar system; I've attached notes from our first lecture- hydrostatic equilibrium. I'm confused about the notation $\mathrm{d}$ for $\mathrm{d}A, \, \mathrm{d}r$, ...
- 1,723
-2
votes
1
answer
84
views
Where did $1/2$ of this come from? [duplicate]
Work done by an external force $F$ upon a particle displacing from point 1 to point 2 is defined as
$$
W_{12} = \int_1^2 F \cdot dr
\, .$$
Kinetic energy and work-energy theorem: According to Newton's ...
- 363k
1
vote
1
answer
76
views
How do force and mass work with all derivatives of position?
I think if $F(t) = kt^0$ then $$x(t) = x_0 + v_0t + \frac{k}{m}\frac{t^2}{2!},$$ and if $F(t) = kt^1$ then $$x(t) = x_0 + v_0t + \frac{k}{m} \frac{t^2}{2!} + \frac{k}{m} \frac{t^3}{3!},$$ and so on, ...
- 12.9k
0
votes
2
answers
81
views
What is $F$ and what is $P$ in the sentence "$F × dP$ is a total differential"?
The physicist Emilio Segrè, as a student, attended lessons of Calculus given by Francesco Severi and of Analytical Mechanics given by Tullio Levi-Civita. Segrè wrote in his autobiography1
For many ...
- 119
0
votes
3
answers
180
views
How do I write the gradient in angular coordinates ($\theta_1$, $\theta_2$, $\theta_3$)?
I have to find $\tau$ by finding the gradient of $U(\theta_1, \theta_2, \theta_3)$, where my coordinates are $(\theta_1, \theta_2, \theta_3)$. I assume the gradient is not the simple Cartesian ...
- 3,358
0
votes
2
answers
236
views
Differentiating displacement with respect to speed in order to obtain time
I have this problem where I am trying to calculate $d(t)$ and $v(t)$ of a mass m on a spring, dropped from a displacement $A$, without using anything else than Hooke's law and energy calculations. ...
- 213k
0
votes
0
answers
145
views
Work-Energy Principle Derivation
I am currently in Mechanics I and both my professor and my book have derived the work principle in this way and I even asked about its derivation during class, but it has me puzzled.
I don't ...
- 213k
1
vote
2
answers
73
views
How do you differentiate this differential equation? [closed]
I have to differentiate this equation (Gravitational force between N-Bodies)
$\begin{align}
\frac{d^2}{dt^2}\vec{r_i}(t)=G
\sum_{k=1}^{n}
\frac
{m_k(\vec{r}_k(t)-\vec{r}_i(t))}
{\lvert\...
- 213k
0
votes
0
answers
147
views
How to calculate the derivative of the angular momentum vector $ d\vec L = d(\hat I \vec \omega)?$
My last question, but also the most important one How to calculate the derivative of the angular momentum vector?
$$ d\vec L = d(\hat I \vec \omega)$$
I'm especially interested in derivative tensor to ...
- 213k
-1
votes
2
answers
603
views
What does $d$ stand for in this formula?
Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am ...
- 213k
2
votes
5
answers
346
views
Significance of $\frac{dv}{dx}=0$
Suppose an object is moving with varying acceleration in time.
What does it mean when it hits a point where $\frac{dv}{dx}=0$?
Does it mean the object has hit maximum velocity?
Assume the object ...
- 8,040
1
vote
1
answer
141
views
What is the difference between zero and an infinitesimal number?
In a standard Atwood machine physics problem, the string going over the pulley is considered massless. So does that imply mass = 0 or mass = dm? General question: what is the difference between 0 and ...
- 2,682
1
vote
1
answer
177
views
Find $v(t)$ and $x(t)$, How do I treat $δt$? [closed]
We apply a force to a particle with a mass $m$ and inicial velocity $v_0$:
$$ F(t) = \left \{ \begin{matrix} 0 & \mbox{ $t<t_0$}
\\ \frac{p_0}{\delta t} & \mbox{ $t_0<t<t_0 +\...
- 3,518
0
votes
3
answers
577
views
What is meant by $dy/y$?
Consider the language in the following example:
What is meant by $dg$ and $dR$, and also by $dg/g$? Why does $dR/R=-2/100$ (negative for shrinks)? Is $4\%$ unity change? I mean $dg/g=4\%$ or $dg=...
- 119k
2
votes
1
answer
1k
views
Taylor series expansion of $\ln$ and $\cosh$ in distance fallen in time $t$ equation
I want to find the Taylor expansion of $y=\frac {V_t^2}{g} \ln(\cosh(\frac{gt}{V_t}))$
I have tried using the fact $\cosh x= \frac {e^x}{2}$ for large t, which works, I just need help on small values ...
- 345