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