All Questions
10
questions
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43
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How can I find the point of balance of an half ellipsoid with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1,\:x\ge 0$
How can I find the point of balance of an half ellipsoid with the equation
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1,\:x\ge 0$$
As point of balance I mean the point on the surface it stays ...
6
votes
2
answers
240
views
How to place optimally four electrons on a sphere?
$\newcommand{\S}{\mathbb{S}^2}$
Let $x_1,x_2,x_3,x_4 \in \mathbb{S}^2$ be points on the unit sphere, that minimizes the quantity
$$
E(x_1,x_2,x_3,x_4)=\sum_{i < j}\frac{1}{\| x_i - x_j \|},
$$
...
- 25.3k
1
vote
1
answer
237
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Is there a way to find the intersection of two rectangles given their current velocity and position in constant time?
Suppose I have two rectangles, let's define them as $R_1$ and $R_2$, which each contain a length and width. Given the headings $\theta_1$ and $\theta_2$ respectively, as well as the coordinates $x_1, ...
- 11
1
vote
0
answers
86
views
Center of mass of an irregular icosahedron
What is the center of mass of a regular icosahedron with edge length $2$ centimeters? The object is one mass, but is divided exactly in half and each half is a different material. One material is ...
- 11
1
vote
2
answers
450
views
Intensity of parabolic reflector as a function of the radius.
I'm trying to make sense of the intensity of light leaving a parabolic reflector, given that the light is a point source at the focus. (In the diagram below, this might be the intensity of light at $...
- 5,072
2
votes
1
answer
91
views
Projected mean (p)-distance from a point to the surface of an (n)-sphere
I am considering a point R inside an sphere of radius 1 in dimension d. The point is at a distance x from the center of the sphere, and the axis 0x is thus defined.
The distance between the point ...
- 31
0
votes
1
answer
150
views
Curvature at a point in a vector valued function
I am trying to determine the curvature when $t=2$ of the function $r(t)=<t^3,3t^2,8t>$
So I found $v(t)=<3t^2,6t,8>$ and $a(t)=<6t,6,0>$. So now that I have these two functions, I ...
- 1,589
0
votes
0
answers
3k
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What is the density of a homogeneous disk with mass $m$ and radius $a$?
Could someone help me understand why the density of a homogeneous disk is $\dfrac{m}{(\pi a)^2}$?
I am trying to understand an example about finding the moment of inertia of an object.
The question ...
2
votes
1
answer
536
views
Moment of inertia of a circle
A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$
Thank you
- 1,341
2
votes
0
answers
2k
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Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= -\...
- 5,527