All Questions
275
questions
2
votes
1
answer
104
views
Calculating deflection on a beam
This is for a hobby project, and to learn a little about elasticity along the way.
I have a triangle wedge comb piece of decreasing width and angle for which the cross section is shown here:
For each ...
- 406
1
vote
0
answers
96
views
Covariant derivative of a Riemann tensor
I'm trying to calculate the covariant derivative of a Riemann tensor, and I'm using the following way, but there is some problem in my calculations because my calculations do not match with the ...
- 11
0
votes
0
answers
29
views
Algebraic varieties associated with (simple) "string" constructions
It is relatively well-known that any arrangement of points that can be constructed with a straightedge and compass can also be constructed with an unstretchable string (of arbitrary length, negligible ...
- 131
4
votes
1
answer
70
views
Modeling Nanotubes Geometry
In various references, we see the construction of unit cells of carbon nanotubes (CNTs) from chiral and translational vectors.
The chiral vector is given as:
$$\vec C_h = n\vec a_1 + m\vec a_2$$
...
- 3,789
1
vote
0
answers
48
views
Clarification Regarding Solid Angle
I am studying Zangwill's Modern Electrodynamics but I'm having trouble following an argument he makes about solid angles in preparation for deriving the integral form of Gauss's law.
He defines the ...
- 319
0
votes
0
answers
33
views
Rearranging trigonometric equation for low speed vehicle turning geometry
I have a set of equations that describe the geometry of a vehicle in low speed turning (a single track vehicle with the assumption that the tyres go in the direction they are pointing). A constraint ...
0
votes
1
answer
36
views
Precisely defining the overlap depth, or deepest point of overlap, for ellipsoids and spheroids
I was wondering if there is a robust mathematical definition for the 'deepest point of overlap' of ellipsoid (or, equally as good, spheroid) 1 that has overlapped with ellipsoid 2. For non-overlapping ...
0
votes
2
answers
122
views
Explain how shall we get a direction at a point on the surface of earth other than north pole using magnetic compass [closed]
The Qibla Compass can give the direction towards "some points on earth" other than north pole, eg : Mecca.
Wikipedia first paragraph, last two lines :
To determine the proper direction, one ...
- 556
1
vote
1
answer
384
views
whats happening when i do arctan? Mistake or wrong in calculator
I have a problem in a solids course about mohrs circle and its principal forces.
I have solved to its last part and it all checks up when putting the right angle theta which makes the shear stresses ...
- 19
2
votes
0
answers
53
views
Optical path of a light ray reflected from two mirrors and into a pinhole camera
I have been staring at this problem for longer than I would like to admit.
I am trying to determine the path of a light ray from an object that is reflected from two plane mirrors and into the ...
- 21
0
votes
0
answers
43
views
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 ...
0
votes
1
answer
147
views
Calculate position of bouncing ball based on arbitrary time value
Usually, when you make a bouncing ball in any programming language, you have an X and Y value that updates over time, as well as an x velocity and y velocity, whose signs flip when the ball hits the ...
- 3
5
votes
1
answer
127
views
Net force on the side of a jar
A round conical flask is filled with water of a depth $h$. The radius of the upper water surface is $R_1$ and that of the lower
surface is $R_2$.
What is the net force that the water exerts on the ...
- 1,043
1
vote
0
answers
56
views
Doubt about Malus Theorem. (Optics)
I'm reading the text "General theory of rectilinear ray systems"
By E. E. Kummer. (http://neo-classical-physics.info/uploads/3/0/6/5/3065888/kummer_-_rectilinear_ray_systems.pdf). I'm new in ...
- 342
1
vote
1
answer
93
views
Problem with the geometry of two balls inside a jar
lets say we have 2 balls inside a jar with radius 1.5, I am trying to calculate the torque with respect to the point of contact of the left ball with the jar.
so far I have that the weight of the ...
4
votes
4
answers
594
views
Ray problem (geometry)
Problem:
Two plane mirrors $OP$ and $OQ$ are inclined at an acute angle (diagram is not to scale). A ray of light $XY$ parallel to $QO$ strikes mirror $OP$ at $Y$. The ray is reflected and hits ...
- 1,755
0
votes
0
answers
19
views
Computation checking: tensor contraction
I'm trying to compute $\langle dx^\mu\wedge dx^\nu, dx^\rho\wedge dx^\sigma \rangle$. This should give give the answer $G^{\mu\rho}G^{\nu\sigma}-G^{\mu\sigma}G^{\nu\rho}$, if we use the formula
$$\...
- 109
2
votes
2
answers
222
views
Is the law of reflection against math?
In my textbook of science (class 10), it is given that for any mirror, the angle of incidence is equal to the angle of reflection.
Here I m talking about spherical mirror. A convex mirror.
All rays ...
- 399
1
vote
0
answers
26
views
Is there a formal name for the shortest (directed) line segment connecting two skew lines?
Is there a formal name for the shortest (directed) line segment connecting two skew lines? I don't believe the dimension of the space matters so long as it is greater than 2. But I am specifically ...
- 3,349
0
votes
0
answers
24
views
The sum of $N-1$ cosines about an $N$-sided polygon? [duplicate]
While studying some physics problems on electrostatics, I derived this curious identity that I am having trouble proving. Show that:
$$
\sum_{n=1}^{N-1} \cos\left(\frac{2\pi{}n}{N}\right)=-1
$$
where, ...
11
votes
1
answer
481
views
Why does a wheel need seven spokes to hold it rigid? (an "inverse problem")
In the biography "King of infinite space: Donald Coxeter, the man who saved geometry" by Siobhan Roberts, the following passage describes an aspect of the subject's relationship with ...
- 1,620
2
votes
1
answer
76
views
How to calculate the center of gravity of multiple weights placed along the perimeter of a circle?
We want to attach n various weights to the perimeter of a circular turbine, equidistant from each other.
I thought about using the cosine function of the position, the weight and the radius somehow (...
- 109
0
votes
1
answer
363
views
How would I accurately simulate orbital motion in desmos? [closed]
Basically, I've been wanting to make a map of a fictional solar system which moves accurately. I have a circle to represent the parent star, a circle representing the planet, which is moving around a ...
- 111
0
votes
1
answer
37
views
The connection Between slope of two connected lines.
So I was working on a very basic physics problem that had something to do with finding the height of a triangle(the velocity vs time graph)
enter image description here
A body starts from rest with an ...
0
votes
0
answers
32
views
Constructing the optical centre point according to given conditions
If we are given the focal length value and also the distance of three collinear points ($A,B,C$ with $AB= BC= 2$ cm , $AC= 4$cm) from focal plane is given and its images from the respective focal ...
- 977
4
votes
3
answers
341
views
geometrical/physical interpretation of multiplication of real numbers (including negative)
In calculus we see that the derivative has a physical interpretation as speed, and a geometric interpretation as slope, and that they are helpful when thinking intuitively about that concept. But this ...
- 27
-1
votes
2
answers
132
views
How much of the earth can see the moon? [closed]
I framed this into 2d. If you draw two circles, get the common direct tangents, then you need to find the angle between the two intersection points for the two lines and the bigger circle. Except I ...
- 83
5
votes
1
answer
796
views
Generalizing Lami's theorem
In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly ...
- 1,011
1
vote
1
answer
75
views
Solving "when are these two exponential trajectories exactly distance ... apart"
I have two exponential functions related to a physics problem where two circles with same radius $r$ that are subject to non-linear drag travel with velocities $v_1=\{x_1,y_1\}$ and $v_2=\{x_2,y_2\}$, ...
1
vote
1
answer
631
views
What is the equation describing earth's orbit around the sun in 3 dimensional space?
I'm trying to draw a 2d ellipse in 3d space, which describes earth's orbit around the sun. such as image of a 2d ellipse in 3d space or the same image but different perspective. I'd like to be able to ...
- 11
0
votes
0
answers
88
views
Calculating a building's shade with building height
I work in GIS and to create a shade layer of a building, I need to "translate" the geometry/building or permanenently move it.
But I just need some help with my formula based on this video.
...
- 101
1
vote
0
answers
38
views
Change orientation of turns of a trajectory
Consider a robot following the dynamical system $R_B'=R_B\exp(\omega_B^{\times}), v_W'=R_B\alpha_B + g_W$, where $R_B\in SO(3), v, \alpha, \omega, g \in \mathbb{R}^3$, and $\omega^\times$ is the skew ...
- 2,109
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
58
views
Geometry: path length in atmosphere ("round" Earth)
I'm having trouble obtaining this physics formula. Since it's mostly about geometry, I hope it isn't out of place here.
I'll paste the text from the book:
Considering the curvature of the Earth (R is ...
- 13
0
votes
1
answer
34
views
Does the resultant vector stay the resultant vector after the drawing of the transversal?
Question:
Two forces of magnitude $4P$ and $3P$ acting at a point O have a resultant of magnitude $5P$. If any transversal cuts the lines of action of the forces at the points R, S, and T respectively,...
- 3,186
2
votes
2
answers
126
views
Confusion regarding volume of fluid displaced by a partially immersed body
Say I have a cylindrical apparatus partially filled with a water column, the height of the column being $h$. Now I have a solid cylinder of radius smaller than the apparatus and height $H>h$ but ...
1
vote
1
answer
68
views
How do I get the time it takes to travel between two points in a circular motion? [closed]
I have two points on a circle.
Circle with two points
Given that I have the constant angular velocity, cartesian coordinates of the two points and center, and the radius. How would I get the time it ...
- 15
0
votes
1
answer
182
views
Expressing $\phi$ and $\theta$ in terms of time difference of arrival
I have an experimental setup consisting of three receivers with known locations $\langle x_i, y_i, z_i \rangle$, and a transmitter with unknown location $\langle x,y,z \rangle$ emitting a signal at ...
- 1,381
1
vote
1
answer
171
views
Ball with diameter collision with inclined wall/plane in 2D Coordinate System
Given the position of a ball, the diameter, a direction/target position and the 4 edges of a rectangle(2:1 ratio) how can I find the end position (coordinates of a point) of a ball if it collides with ...
0
votes
1
answer
105
views
Tilting a mass suspended on 2 springs
I was trying to model the following problem:
There is a solid brick shaped body, with center of mass $(x,y,z)$. We put this body onto 2 springs. For making the problem easier, we cut out the slice ...
0
votes
1
answer
84
views
Ultrasonic anemometer: Transformation of space diagonal components to Cartesian components
We have built an ultrasonic anemometer measuring 4 components of air velocity along the 4 space diagonals of a cube. The space diagonals can be characterized by vectors (1,1,1), (1,-1,1), (-1,1,1) and ...
- 31
5
votes
3
answers
236
views
Relations Between Probability Distributions and Physical Phenomena
I have created a $3$-dimensional visualization of the Central Limit Theorem in Mathematica...
However, when flipped upside down, from below it looks suspiciously like light being emitted from a ...
- 1,922
1
vote
1
answer
314
views
Maximum horizontal force that does not cause block to slide up ramp
You are sliding a block with mass m up a ramp inclined at an angle of $\theta$ with respect to the horizontal where the coefficient of static friction between the block and the ramp is $\mu_s$. What ...
- 1,225
3
votes
0
answers
37
views
Smallest Polymer that can Pass through a Circular Orifice
In a microfluidic setting, I have encountered a puzzle of finding the minimum size (smallest total-length $L$) of a polymer (can be hyperbranched or loop, whatever shape that you can make from merging ...
- 81
6
votes
2
answers
190
views
When do two triangles reflected over midpoints have the same area?
Suppose I have a triangle ABC. I have points C', A', and B' on segments AB, BC, and CA, respectively. Suppose I reflect C' about the midpoint of AB to get point C'' (also on AB); similarly for the ...
1
vote
1
answer
69
views
Calculating angle from sphere
I'm trying to calculate the angle Phi in the picture in the case where the droplet is the perfect sphere I have the correct formula but I'm not sure how they found it. and I want to know the formula ...
- 29
1
vote
1
answer
101
views
A possible new type of interference pattern?
In quantum mechanics, one often encounters complex interference patterns.
Here, I am curious about geometric interference patterns. For instance, let me define two wave-functions:
$$
\psi_1 = \exp (...
- 2,589
7
votes
0
answers
121
views
Shape of very long wire between two very tall posts (many km tall) which are attached to the earth
Consider for a moment a length of uniform wire or chain which goes between two posts of equal height. If we assume the earth to be flat then we can predict the shape of the curve using
$$y = a \cosh \...
- 181
0
votes
2
answers
432
views
How to generate random velocity vectors that can only move an object forward within a valid arc?
I have an object with known coordinates in in 3D but on the ground (z=0). The object has a direction vector. My goal is to move this object on the ground (so ...
- 435
0
votes
1
answer
55
views
Relation between force, vectors and coordinates
I have the following exercise in my math book:
A $1000\,\mathrm{kg}$ barrel hangs from a hoist. At the hoist $AC$ and $BC$ are rods and $DC$ is a steel cable. Determine the forces in the rods and the ...
- 55