In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r.
d
=
2
r
⇒
r
=
d
2
.
{\displaystyle d=2r\quad \Rightarrow \quad r={\frac {d}{2}}.}
For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.
For an ellipse, the standard terminology is different. A diameter of an ellipse is any chord passing through the centre of the ellipse. For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis.
The word "diameter" is derived from Ancient Greek: διάμετρος (diametros), "diameter of a circle", from διά (dia), "across, through" and μέτρον (metron), "measure". It is often abbreviated DIA, dia, d, or ⌀.
I really do not understand what they are asking here...wording here in english is a bit confusing to me...but from similar examples, i made use of the approach below (which i still do not understand) hence my post.
##\dfrac{30π}{60 ×180} = \dfrac{0.0254}{d}##
##d = \dfrac{274.32}{30π}##
##d=...
Hello,
I'm trying to help my kiddo with some math, and unfortunately this is stumping me.
A full reel of cable has a diameter of 60 inches. A job requires 314 feet of cable. How many turns of cable should be taken off the the reel?
The answer is 20 turns, but I can't seem to figure out how...
https://phys.org/news/2023-03-massive-giant-exoplanet-tess.html
It is one of the most massive and densest exoplanets. For comparison, Mo has a density of 10.22 g/cm3 and Ta has a density of 16.6 g/cm3. I would suspect that some of the density is derived from the high compressive pressure of...
Greetings,
I've come across lots of exercises regarding Bernoulli's equation. However, never seen one where the top of the vessel is closed, and fluid flow exists via gas (air) going in. Has this problem been studied in the past?
Assume a cylindrical vessel filled to the maximum with a D-sized...
Alright, this is more of a conceptual question than a HW question that will nonetheless help me design something. In the attached image, air is flowing through a large area tube and then a small area tube from right to left. A collaborator previously figured out the equation for measuring the...
I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning:
1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2).
2) F= stress/area. Force (load is the same). If cross sectional area...
I have a friend who wants to replace his scope. Has a balcony overlooking the lake, so less about stars; more about Moon and terrestrial. So he's interested in a (right side up) refractor. He can save on the mount by getting an alt-az instead of an eq.
He's looking at this 4" Celestron...
Probably, to satisfy the significant digits rule for division, we should consider ##r = 5.0 \div 2.0##. But I'm unable to come up with a reason why significant digits rule should not apply to ##r= d \div 2##. Also, if we apply significant digits rule to this calculation then we loose accuracy...
Hi all, I'm a tinkerer with no formal engineering background, but enjoy read about physics and engineering in general.
I'm reading up on fluid flow and I'm a bit grasping at the concepts. As far as I understand it, flow rate, pressure drop and pipe size are all interrelated, where one affects...
Imagine a bolted joint with a washer between the bolt and the surface.
Assuming the washer is always covered by the bolt head so it's getting a consistent load, does the washer's diameter impact the static friction being imparted on the surface?
I see two conflicting ways of viewing this...
I have a empty bottle and immersed it into the water, where the pressure inside the bottle is equal to air pressure. If I want to make a hole on the bottle, how big is the hole to prevent the water leak into the bottle at different depth?
what kind of parameter is involve in this phenomena? can...
I would like to know how to calculate, for any specified frequency in Hz, the required diameter of a 90 degree phased, quadrature coil array such that its generated EM field achieves rotation at the speed of light.
Could someone please provide an example of the calculation using a specific...
Hi All
I'm sure this question has been covered previously , but when searching I do not find a definitive answers.
I recently watch some talks given by Kip Thorne that had me thinking about black holes and their densities.
So my deduction is as follows .
Using General relativity, and...
I need to prove the above statement. I have a very strong gut feeling that the above equation is not true, and so I need to find a case where the graph diameter is greater than the average pairwise distance.
First off, I would like to clarify about the average pairwise distance, which is given...
What is the method of calculating the diameter of a solar system knowing each of its planets distance to the star? Is it a matter of doubling the distance of the furthest planet?
What about when a solar system has more than one star?
So I know current is just coulombs/second. Electrons are also in the unit of coulombs, so I can get coulombs to cancel.
7.9C/s/1.602E-29C = 4.93133E29 1/s
Now I just need to get mol on top. There are 6.022E23 electron in a mol so 4.93133E29 1/s / 6.022E23 atoms/mol = 8.1889E5 mol/s.
Now my...
I am writing an article about the Hubble Tension and when I was looking through the angular diameter distance I get confused over something.
In many articles the angular diamater distance to the LSS defined as the
$$D_A^* = \frac{r_s^*}{\theta_s^*}$$ where ##r_s^*## is the comoving sound...
Hello,
I am trying to change a 0.9mm screw with a 1.0mm screw. The material is 18k gold, and so the hole is to be threaded.
Is it ill advised to force the larger screw in without tapping the smaller hole? the difference in screw size is just .1mm, and we assume the thread pitches are...
Least count of the screw gauge = Pitch÷No. of divisions on circular scale=1.5÷100 mm =0.015mm
According to me,in this case the main scale reading should be taken as 2 mm because it is the one which is visible and circular scale reading should be 76.
So, Diameter=2 mm + 0.015×76 mm
= 2 mm + 1.14...
I am confused because the question implies that I need to do some sort of calculation with Kepler's law. I got
##r+d = \sqrt[3]{\frac{T^2 GM}{4 \pi^2} } ##
But don't understand why I need this, since I already have the distance and the angular diameter should be ##\arctan (2R/d)## I think I...
Is there a limit on the minimum diameter that a collimated electromagnetic beam must have (lasers or masers), in terms of its wavelength, or it is possible to create a beam with its diameter smaller than its wavelength?
I'm considering a colimated planar wave directly from the source, and not...
Hello all this is my first post. I am not an engineer, but I wish I was. I have been enjoying watching Dan Gelbart!s YouTube Chanel. His air bearing has me wondering about the relationship and apparent conflict inside ball bearings. How does the ball travel around the shorter distance...
Hello,
So we are designing a turbine. We have a shaft that receives 710W / 13.6NM / 500RPM from the runner and we are going to find a diameter with safety factor of 3.
Take the following information regarding metal:
Aluminium 6061
Tensile strength
115 MPa
Yield strength
48 MPa
Shear...
Source: fobasics.blogspot.com
Source: scirp.org As it is shown in the first pic above that the mode field diameter is defined as the mode field decreases to 1/e (in intensity 1/e^2), if I take the mode field and subtract the core's diameter then I divide it by 2, should I get the penetration...
Can anyone help me in what assumptions I can make and how to justify them for when working out diameter of the molecule in part b) of this question? You can see the method that I have used in my workings but how would I explain it in words?
I obtained the diameter to be 0.13 nano metres which...
Hello. I have figured out a few things about ST-type exchangers and I intend to build a reactor with this new knowledge. I have a rather... small problem.
So I searched for shell diameter correlations given the pitch and number of tubes and I found this from a writeup:
Apparently, it's from...
Mentor node: Added code tags
From=menu('select:','c', 'g', 'a', 's:'); This is part of my code and I'm not coming up with anything close
l=input('input wire length') %current copper=12.5572...
Hello.
My attempt at the solution is as follows:
l = 160m
Q= 300 ls-1
R= p2/p1= 6+1.01/1.01 = 6.94 (2dp)
d = Unknown
Pressure drop = 0.3 Bar
0.3 = 800*160*300^2/6.94*d^5.31
0.3 = 1.152x10^10/6.94*d^5.31
0.3 ( 6.94*d^5.31) = 1.152x10^10
6.94*d^5.31 = 1.152x10^10/0.3
d^5.31 =...
I have attached an Excel-worksheet in which the problem should be clearified. The problem concerns the calculation of the bending moment acting in a pin in double shear, experiencing a certain load from a hydraulic cylinder. The plate thicknesses should be taken into account. Specifications and...
Hi!
I would like to know how to exactly calculate required wire diameter? For example, here I found this calculator on internet: https://www.solar-wind.co.uk/CST.html .
It takes acceptable loss, volts, amps, and cable length for arguments. It specifies Vdc. Would it be different formula with...
If particle accelerators with circumference of the Earth could be built (imagine around the world). How many TeV can it reach? Maybe new physics can occur at 2000 TeV.
I heard the US nuclear arsenals costs 2 trillion dollars. Worldwide, the total costs of all nations nuclear arsenals may reach...
I'm trying to determine if a certain bicycle tire size will fit my bike, and that determination is based on the inflated diameter (or width) of the tire. As such, I'm trying to come up with a formula that will give me the diameter of a bicycle tire as a function of the tire's carcass width and...
According to this link (https://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/collisions.htm) the LHC achieves a beam waist diameter of approximately 64 microns. What limits them from getting a tighter focal point? Are lower energy beams easier or harder to focus tightly?
Summary: Looking of someone to double check my work on this design issue.
I am posting this here because I am no longer a student, but it is similar to a simple homework problem
Problem: I am designing a rubber-band like product for a client. He wants to take a durable rubber band and stretch...
Hello,
How to determine the pulley diameters? The only know factors are listed below.
The smaller pulley is attached to a motor that drives the belt drive system. The bigger pulley is driven and has a lifting force of 45N.
Known factors:
Motor: Pololu 70:1 37Dx54L mm 12V...
I have found plenty of information about the radio source Hercules A. Its large radio jets are 1.5 million light years long from end to end, the supermassive black hole that produces Hercules A is 3 to 4 billion solar masses, and the black hole exists in the center of galaxy 3C 348. However, I...
A circle is inscribed in a square with sides = 40.
A smaller (of course!) circle tangent to the above
circle and 2 sides of the square is inscribed in
one of the corners of the square.
What is the diameter of this circle?
How do you increase torque in gerotor design other than increasing flow. Will lengthening it increase torque? Will increasing diameter increase torque? What about running 2 or 3 in series?
Hi I am doing an electron gun diffraction right now and I wonder why the angle below is 2 phi.
What I think about it that it's actually the results of two waves one is shown below and the other is a wave
with the same accident angle but negative "those two rays will be symmetric around the...
Textbooks say it decreases flow. But, when I think about it...
If you blow through a small straw, you are blowing out less volume. But wouldn't the speed of flow be higher, therefore making up for the decrease in volume?
Like this:
Lower volume squeezed out faster = higher volume squeezed out...
This was a MCQ question on one of my Cambridge IGCSE Exams, the answer key said that the resistance would decrease by 16 folds (1/16 less then the previous one), I don't know how they got 16 from? (Apparently, I answered 1/4 and it was wrong)