All Questions
Tagged with calculus classical-mechanics
8
questions with no upvoted or accepted answers
2
votes
2
answers
825
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Necessary and Sufficient Conditions for an Equilibrium to be Stable
In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement:
For the (mechanical) equilibrium to be stable, it is ...
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1
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Is $n_{cr}=\frac{60}{2\pi}\sqrt{g\frac{\Sigma m_iy_i}{\Sigma m_iy_i^2}} =\frac{60}{2\pi}\sqrt{g\frac{\int y_idx}{\int y_i^2dx}}\quad ?$
I have a question about this formula used to calculate the first critical speed of a drive shaft.
$$
n_{cr}=\frac{60}{2\pi}\sqrt{g\frac{\Sigma m_iy_i}{\Sigma m_iy_i^2}} \tag {1} \quad .$$
It is the ...
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Question on non-holonomic constraints (This is different to the others)
I know there are many posts on non-holonomic constraints and also many on this exact one but I feel that there is still some confusion on it.
"Consider a disk which rolls without slipping across ...
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Time to travel a set distance given variable acceleration
Trying to solve a problem for the acceleration of an automated shuttle car at my work, been a while since I studied this stuff so thought I'd reach out for help.
I have a shuttle car that is tasked ...
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Minimum seperation of moving objects doubt
Let there be $2$ objects $P_1$(initial velocity $u$ $ms^{-1}$ & acceleration $a$ $ms^{-2}$) & $P_2$ (initial velocity $U$ $ms^{-1}$ & acceleration $A$ $ms^{-2}$) initially separated by ...
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2
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Contact surface between circle and curved floor?
First, consider an inelastic circle on a hard, flat floor, the shared contact surface between the two is some infinitesimally small length dx.
Consider a second case, where if the floor had some ...
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1
answer
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Can a position variable have an infintesimal in it?
I've been pondering unstable systems, such as a perfectly round rock atop a smooth hill. At the top of the hill is a metastable point where the rock could roll either way after an arbitrary amount of ...
- 50.1k
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Working with infinitesimal quantities and the motivation behind it
So in my freshman physics class, in classical mechanics the homework was (it's solved already, this isn't a homework thread) the following:
"A thin, spinning ring is placed on a table, that divides ...
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