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5
questions
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Tidal forces mathematics
Let's calculate the difference in force, $\Delta F$, experienced by
the rocks. Because $\Delta r$ is very small compared to $r$,
$$\Delta F = F_{\text{out}} - F_{\text{in}} \approx\frac{dF}{dr}\Delta ...
0
votes
1
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Doubt in finding center of mass of extended bodies [closed]
While finding center of mass of extended bodies, we generally write the coordinate of the starting point of the infinitesimal mass element. Why not the ending or starting point? How does the error ...
0
votes
1
answer
141
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Differential Equation & MacLaurin Series for Newton’s Second Law
I am currently working with a differential equation, where I think I need to take the derivative of $ma$ (corrected as per comment). I am trying to write $F = ma$ as a MacLaurin series and eventually ...
- 151
1
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1
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141
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Can you 'derive' mathematical approximations made from Taylor approximations from limiting cases in real life?
Here, the natural length of the string is $l_o$, and pulling the string up by $x$ increases its length by $ \sqrt{ l_{o}^{2} +x^2}$; thus, the increase in length can be approximated as
$$ \delta l = \...
- 7,980
4
votes
1
answer
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How does the small angle approximation work for cosine?
In newtonian mechanics equation of motion of a simple pendulum:
$$\ddot{\theta}=\frac{g}{l}\sin\theta$$
And then I approximated for small angles $\sin\theta\simeq\theta$ that yields the equation of ...
- 1,989