1
vote
1answer
21 views

The weight of a drilled out cylinder

Cylinder is $2.71$kg or $2710$g, diameter is $5$cm and $7.5$cm high. The volume is $147.18$cm$^3$ and the density is just the mass divided by the volume, I'm not sure if I need to convert it into ...
0
votes
2answers
23 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
1
vote
3answers
258 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
0
votes
0answers
37 views

Strange question about magnetic dipole in a plane at infinite distance

Please allow me to ask something rather unusual and perhaps completely naive. Suppose I have an electric current in a circular loop in a plane. Consider it just in a mathematical sense, i.e. an ...
1
vote
2answers
68 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
6
votes
1answer
104 views

Why do objects that are farther away look smaller?

What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
0
votes
0answers
38 views

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 ...
4
votes
0answers
42 views

How to integrate scalar field over quarter torus? Infinite series does not converge.

This seems to be physics question, but the problem just concerns math. Preface If one wants to calculate the permeance $P$ of a rectangular bar: it is an easy task: $$P = \frac{\mu a b}{L} ...
0
votes
0answers
47 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
1
vote
1answer
34 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
0
votes
1answer
25 views

Calculating the force on each of two directions needed to move object to destination

Given the following: How would you calculate the forces needed on the v and u directions to move point ...
1
vote
3answers
100 views

Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
0
votes
1answer
67 views

Please, as possible, explain in layman's terms: What is a discontinuous space?

What is a "discontinuous space"? Is it synonymous of "discrete space"? I searched in Google but did not find an accessible explanation. I have an idea of it as a space where all lengths are multiples ...
6
votes
1answer
81 views

Platonic solids and charged particles

It is known that there are five Platonic solids: If, lets say, there are 4 particles with the same electricity charge and whose movement is constrained to be on a sphere, resulting forces will ...
4
votes
2answers
125 views

Why do folded concentric circles and rectangles form a hyperbolic paraboloid?

Here is a "self-forming" origami that I made from folding concentric circles - it would also happen if I folded concentric rectangles. How can the fold shapes such a saddle-like geometry?
-1
votes
2answers
100 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
2
votes
0answers
68 views

What if segments are not infinitely divisible?

I almost got myself mixed up I a philosophical discussion again. Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how ...
0
votes
1answer
26 views

Fastest direction in circular trajectory [closed]

I have a point P and a vector V. This point is describing a uniform circular trajectory with linear velocity lv and angular velocity av. This trajectory passes through a point P', how do I find out if ...
1
vote
2answers
174 views

Area under the Trajectory of a projectile

I may need some help with the following problem. We have $$ y(\omega)=a+\omega\cdot b - \frac{1}{2}\cdot\omega^2\cdot g $$ where $g$ is the gravity vector $g=\binom{0}{\lambda}$, $\lambda \approx ...
0
votes
1answer
76 views

Finding angle on an inclined plane

How can I go about finding the angle, theta, in this Physics problem? As you can tell, the right-most triangle is a simple 30-60-90 triangle, so above the right angle is a 60deg angle. Then the ...
0
votes
1answer
65 views

Elliptical polarisation

In physic context one find the curve with parametrisation in t, $x=x_0\cos(t)$ and $y=y_0\cos(t+\varphi)$ with is an ellipse with equation ...
4
votes
0answers
82 views

A light beam enters a closed room. What is the maximal number of reflections?

I have the following problem: a light beam enters a mirror room with integer coordinates in the plane (consider it as a polygon). One of the walls of the room is removed and the light beam enters the ...
0
votes
2answers
218 views

How to prove the two angles are equal?

It is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triagle have $90^0$ but what about others. If we ...
0
votes
0answers
81 views

The Graphic Representation of Physical Quantities (Vectors only)

We usually use the figure such as the one below for the graphic representation of physical quantities such as forces: What should we call this figure? Should we call it a ray? But a ray is defined ...
2
votes
1answer
756 views

Throwing a Projectile in 2D space

Normally I am strong at maths, but here I have a Math question that after spending 5 pages, I just can't figure it out. Here goes: A person is playing a game that requires throwing an object onto a ...
-4
votes
1answer
169 views

A car drives north, then east, then southwest. Find the displacement and average velocity

A car drives north at 36mi/h for 10 min and then turns east and goes 5.0 mi at 66mi/h . Finally, it goes southwest at 32mi/h for 6.0 min. Find the car's displacement and find the average ...
2
votes
0answers
96 views

Bending of track in a racing game

I am trying to create a small racing game in which the track would be modeled using a BSpline curve for the path's center line and directional vectors to define the 'bending' of the track at each ...
2
votes
3answers
326 views

What is the relation between vectors in physics and algebra?

Vector math is something I find very interesting. However, we have never been told the link between vectors in physics (usually represented as arrows, e.g. a force vector) and in algebra (e.g. ...
1
vote
1answer
178 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
vote
1answer
608 views

Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
2
votes
1answer
175 views

Geometry brain teaser (Candle in the room with mirrored walls)

King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there ...
1
vote
1answer
169 views

Bullseye-shaped interference pattern in seminar-room chair

During a break n a seminar today, I noticed that the chairs in front of me all had slightly transparent black mesh fabric. The backs of the chairs were in the shape of a hyperbolic paraboloid. The ...
1
vote
1answer
104 views

Find initial vector for shell so that it hits desired target

Backstory: We are shooting a cannon from a moving platform (e.g., a ship). Platform velocity is $p$. We know where our target is in relation to us (vector $t$) We know the velocity of our shell ...
3
votes
1answer
252 views

Is there a non-variational derivation of Snell's law from Fermat's principle?

Every proof I've seen of Snell's law from Fermat's principle uses some sort of variational argument, mostly involving variational calculus. Niven's wonderful book, Maxima and Minima Without Calculus ...
3
votes
2answers
528 views

Resolving vectors into components

The problem is to determine the components of $F_2$. Problem image Method 1 Method 2 My question is why do I receive different answers?
2
votes
0answers
665 views

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= ...
2
votes
1answer
939 views

Earth-Sun distance equation

I was studying solar geometry and I read the next equation $$r=r_{0}\left(1+0,017\sin\left[\frac{2\pi(d_{n}-93)}{365}\right]\right) $$ where $r_{0}$ is the average distance between the Earth and the ...
2
votes
4answers
2k views

Why are these angles equal for object on inclined plane?

This is a common setup for kinematics problems in physics. My geometry is rusty and I want to understand this very simple idea. I am having trouble understanding why the angle $\theta$ formed by ...
17
votes
5answers
793 views

What Mathematics questions can be better solved with concepts from Physics?

Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
1
vote
1answer
237 views

Circular motion “calculate the angle”

I have a equation i need to find out how they hang together. angel = (velocity * time) - (acceleration * time * time / 2) I know circumference of a circle: ...
0
votes
1answer
139 views

Parabolas and projectiles

Given $2$ points, $A$ and $B$, if I am in $A$ and I have an inclination angle $c$, with how many velocity do I need to shoot a projectile to hit $B$ ? My problem is, how do I setup this data in an ...
2
votes
0answers
290 views

On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*

When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the ...
3
votes
0answers
524 views

Maximum Jump Distance and Height in Mission Impossible 3 [closed]

In the movie Mission Impossible 3, the main character Ethan Hunt tries to enter a building in Shanghai by swing through the sky, as shown below: The jump consists of 2 sections, the red part, which ...
8
votes
1answer
492 views

Does apparent retrograde motion of planets begin and end at quadrature?

I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
2
votes
2answers
270 views

What is the geometric, physical or other meaning of the tetration?

What is the geometric, physical or other meaning of the tetration or more high hyperoperations? Is it exists in general or it has only math concept?
2
votes
2answers
103 views

Ball from platform with specific vertex

On earth in a vacuum. You throw a platon from a platform height $h$ and want it to land at point $d$ distant. Note, h is absolutely fixed and d is absolutely fixed. It "must land" at point d, no ...
8
votes
2answers
604 views

Fireworks under inverse-cube gravity

What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...
0
votes
1answer
197 views

Is there a difference between shape geometry and spatial geometry in the universe?

My friend posed the question: "How can we construct a 4-dimensional shape [such as the tesseract, the 4-dimensional analog of the cube] when the 4th dimension is time?" My answer was that surely ...
1
vote
1answer
88 views

The Law of Sines and a second forces magnitude

How do you solve for the second forces magnitude? The 17' and 30' threw me off.
6
votes
0answers
102 views

Analytic caustics for 3D objects

Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube? To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...