# Tagged Questions

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

128 views

### Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
130 views

### Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
68 views

### If the Earth were a pool ball, could I feel mountains? [closed]

If the earth (12,742 km diameter) were scaled down to the size of a pool ball (61mm diameter), the mountain ranges would still exist, obviously. But would a typical human be able to feel those ...
68 views

### Finding angle between two displacements [closed]

Consider two displacements, one of magnitude 6 m and another of magnitude 8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 14 m, (b) 2 m, ...
273 views

### Bicycle counter-intuitive: in which direction it will move? [duplicate]

I saw this puzzle in a local newspaper: Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the ...
53 views

### Terminology - optical (visual) properties of a structure

I am trying to understand few terminological problems that I encounter. Without knowing keywords it is hard to perform search for literature or publications in the area. The area relates to the ...
41 views

### The Ehrenfest Paradox and Euclidian Assumptions [duplicate]

As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", ...
49 views

### Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
38 views

### Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever (...
43 views

### The relationship between abstract geometrical concepts and reality? [closed]

In pure geometry points have no parts, lines no breadth and surfaces no thickness, geometrical figures can be exactly congruent. But how do these concepts relate to the physical world. What is the ...
47 views

### Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
57 views

### 3D donuts and the centre of a black hole [closed]

I have been trying to imagine ways to visualise the gravitational field of the earth... It's near zero at the outer edges of the atmosphere, strong at sea level, strongest at the quarter point, then ...
70 views

### When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
75 views

### Relative motion of an arbitrary volume of space ( is space static or dynamic?) [closed]

Do physicists consider space as being "static" or "dynamic" ? Hi I asked a question about whether space can move, and from the answer, I realized I was not precise enough and did not actually ask ...
24 views

### Angular current in torus

I'm trying to find the magnetic field due to a torus anywhere in space. I'm approximating it as a circular current loop. What I'm having a hard time with is the current in the theta direction, that is,...
137 views

### Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
88 views

1k views

### Land proportions in NASA blue marble photographs

What is the explanation for the apparent size difference of North America in these two photos from NASA? Image source Image source
4k views

### How big are clouds? [closed]

How big are clouds? When I look up into the sky I have no frame of reference, so I don't know if they are 200 feet or 2 miles across. When I am in a plane looking out at a cloud, I try to use the wing ...
487 views

### How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
60 views

### Order of magnitude for the range of vision

Let's say you're in the middle of a desert, with nothing but sand. Let's also assume that you have a 20/20 vision. When you're just looking there's a point that your eye can't reach name it $M$ and ...
492 views

42 views

### What is the scale factor of a hyperbolic universe?

I wanted to derive the solution to this question from the Friedmann equations myself but I ran into some trouble. I was working in natural units where $c=G=1$, then, for brevity, I defined f(t)=\...
37 views

### Rate of change in size: Moving Objects

Is there a way of calculating the rate at which an object decreases/increases in size relative to the observer. For example, if a bus(4m wide) is moving away from a stationary observer at the rate of ...
Everyone of us know about the vector cross product. But I wonder, how the formula of $AB\sin\theta$ has been derived? Can anyone help?