Formula Definition and 1000 Threads

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula(often referred to as a well-formed formula) is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:




V
=


4
3


π

r

3




{\displaystyle V={\frac {4}{3}}\pi r^{3}}
.Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form.In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O−3 denotes an ozone molecule consisting of three oxygen atoms and a net negative charge.
In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula

F = mais an expression of Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be liken to phrases the same way formulas can be liken to grammatical sentences.

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  1. P

    A Formula for calculating neutron flux?

    I have a liquid scintillator, the electronics system, and a beam of neutrons from a reactor. How do I calculate the neutron flux? Cold anybody give me a formula or equation? Not this equation: phi = n X v, where phi - flux, n = number of neutrons per cm3, v = velocity of the neutrons, because I...
  2. Trec93

    Problem with equation / proving formula

    Homework Statement I have to prove some formula, I got stuck in the process. Homework Equations Formula to prove: v_{0} = \frac{M+m}{m}\sqrt{2gus} Valid equation that should get me to this formula: \frac{m^2v_{0}^2}{2(M+m)} = gmus The Attempt at a Solution v_{0}^2=\frac{2(M+m)}{m^2}gmus...
  3. S

    Centripetal Acceleration formula derivation

    Hello, This is a very basic question. I am sure I am doing something wrong in the derivation as shown in the picture. But I am not able to find out where I am doing it wrong. It would be very helpful if you can pls. let me know what I am doing wrong here. Thanks
  4. F

    What Does Number of Diameters Mean in Pipe Flow Analysis?

    Homework Statement what is the meaning of number of diameter N ? why the author make L = ND ? and then divide it by D ? Homework EquationsThe Attempt at a Solution
  5. e2m2a

    I Right Triangle and the Pythagorean Triple Formula

    Given: A right triangle and all the sides of the triangle are whole numbers. Does this imply that all the sides of the triangle can only be found by using the Pythagorean triple formula? Another words, is it possible that a right triangle can exist with whole number sides that escape the...
  6. Trec93

    Doppler effect Formula manipulation

    Homework Statement I have this Doppler effect formula, but I don't know how it was derived, I can't repeat the process myself to solve for speed of the source, I would really appreciate if someone could mathematicly solve this in steps, thank you very much. Homework Equations...
  7. A

    Formula to assess wear due to friction in sheaves/pulleys

    Hi everyone and greetings from a new member. I'm looking for informations about how to estimate the wear due to friction of a rope as it passes through a pulley. Couldn't find anything really consistent about the subject. I looked at the capstan and Archard equations but didn't manage to link...
  8. P

    Rearranging an SUVAT Equation: Solving for Time

    Hello everyone, Please can someone help me rearrange this equation to make t the subject: Relevant equations: My attempt at a solution: Thank you all for you help
  9. AndresPB

    I Medical Physics Question about the formula D(x)=alfa*mu*I(x)/rho

    Hello I had two doubts, I know that medical physicist when working with x-rays use the formula D(x)=alfa*mu*I(x)/rho where D(x) is the dosis absorbed Alfa is the factor of the energy that damages Rho is the density mu is the absorbtion coefficient My doubt is the following: Does this formula...
  10. M

    I Hydrogen Atom Photon Emission Wavelength Formula

    I am trying to calculate the Lyman-alpha wavelengths of photons emitted from different hydrogen-like atoms such as deuterium and positive helium ion 4He+, using the relation 1/λ = R*|1/ni^2 - 1/nf^2|, where R is the Rydberg constant and ni and nf are integer numbers corresponding to the initial...
  11. I

    Question about where a thermodynamics formula comes from

    Homework Statement How do we obtain: w = q - Δh Homework Equations The Attempt at a Solution If you neglect the second half of the SFEE and simplify we get: What is the next step from the last line in the above image to w = q - Δh I mean dw/dt = dq/dt - Δh so if we multiply by dt we...
  12. T

    MHB Find a formula for the Riemann sum and take the limit of the sum as n->infinite

    For the function given below find a formula for the Riemann sum obtained by dividing the interval [1,5] into n equal subintervals and using the right-hand endpoint for each c subscript k. Then take a limit of thissum as n-> infinite to calculate the area under the curve over [1,5]. Below you...
  13. F

    MHB Im back with change subject of formula

    so I've been taught basic rearranging of formula which I've found easy now I am given questions which are obviously a lot harder and I've entered the mind black hole if you could point me in the right direction with this where I go wrong make L the subject $f=\frac{1}{2\pi}$...
  14. F

    MHB Changing subject of formula help sites

    hi all ,does anyone know of good learning resources for rearranging formula ,starting from the basic level all the way to advanced levels ? many thanks
  15. F

    Formula of friction loss due to expansion

    Homework Statement in the first picture , K_L = [ [(1/C) -1] ^2 ] taking the diagram in the first picture as an example , the K_l = [(1- (Asmall/ Abig)) ^2 ] , the A small represent the area at A2 , Abig = A1 ? Am i right ? Homework EquationsThe Attempt at a Solution
  16. NickTesla

    Capacitor Discharge Time Formula Euler

    I would like to understand how the Euler constant elevated to fractional exponent gave this result? 958mV someone please!?
  17. grandpa2390

    Solve Manipulate Formula Homework for U+PV to (∂H/∂U)_P

    Homework Statement begin with ##H = U+PV##. Manipulate it into the form: ##(\frac{∂H}{∂U})_P## hint: you might find the resulting expression from part a useful) the resulting expression that I found was ##(\frac{∂U}{∂V})_P = \frac{C_V}{V*a} + π_T##Homework Equations ##π_T## =...
  18. G

    I Creating a formula for the cost of pollution through time

    Apologies if this is in the wrong section. Wasn't sure where to put it. While this is technically homework, I don't think it fits in the homework section In a paper I'm writing, I need to estimate the cost to society of future pollution. Reading relevant academic articles, it seems pretty clear...
  19. F

    MHB Transpose Formula: Solve x=7-2y | Get Help Now

    Hi,thanks in advance for your help Ive been given the task to transpose To make x the subject from y=7-2x Which in my mind x= 7+y / 2 But my book is saying X=7-y / 2 Is the book correct if so where / why am I going wrong ?
  20. F

    Head loss formula in series pipe

    Homework Statement i know that the formula of head loss is (V^2) / 2g , where v =velocity , but , why did the author want to change it to k[(Q)^1/n ] ? Homework EquationsThe Attempt at a Solution
  21. M

    B Limit using the Sohotski-Plemenj formula

    Hi All, I am desperate to understand a calculation presented in a paper by Sethna, "Elastic theory has zero radius of convergence", freely available online $$ lim_{\epsilon \to +0}Z(-P+i\epsilon) = lim_{\epsilon \to +0} \int_{0}^{\infty} \mathrm{d}x \, \int_{0}^{\infty} \mathrm{d}y \exp \{...
  22. F

    Formula of energy per unit weight

    Homework Statement is the equation in the 3rd photo wrong ? since there are 2 exits , why shouldn't the eqaution become (P1 / y) + z + (8.33^2) / (2x9.81) = 0 + z +[ 2 (12^2) / (2x9.81) ] ? Homework EquationsThe Attempt at a Solution
  23. S

    Calculation of torque of engine (mathematically)

    We have tried to convert a petrol engine into a compressed air engine back in our graduation project. At that time we only measured the RPM of engine using tachometer and pressure of compressed air using pressure gauge. Now, we need to know the power of wngine at those readings. As the setup is...
  24. karimce

    About the formula of pendulum -- What if there is damping?

    http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ] a(t) : the angle in instant t . t : time g : gravity . Pi = 3.14 k = Fixed (Friction ) l : longer of pendulum...
  25. LLT71

    B Why don't we use arc length formula to calculate wavelength?

    can you please explain me why don't we use arc length formula to calculate wavelength? seems a bit confusing...
  26. F

    Shear Stress Formula: Calculating Tau Correctly

    how to get the formula of shear stress (tau) ? i got (-dp/ds -ydz/ds )(r/2) instead of -d(p+yz)/ ds (r/2) as in the book , if it's d(p+yz)/ ds (r/2) m , i would get (-dp/ds -ydz/ds-z(dy/ds) )(r/2) ,, right ? The Attempt at a Solution P/s : I'm concerned about the derivation part , so i didnt...
  27. Y

    A Periodic Function Looks Like This Formula?

    My book says this: I don't understand how this works. I learned that the usual sunisoidal function looks like sin(wt+phi), where w is frequency, t is time, and phi is some offset. EQ 17.1 doesn't match the bolded formula above. How does this work?
  28. L

    Backwards extension torque wrench formula + cheat sheet review

    Hello! I took a quality certification test yesterday and there was a question on there about torque wrench formulas. I didn't have anything about that in my notes, so I took some time this morning to create a cheat sheet based on what I could find on the web. 1) In some of the forums, they...
  29. F

    Is I/V Submerged a Valid Formula for Calculating Metacentric Height?

    Homework Statement is I/ V ( in the second picture)submerged is a valid formula of metacentric height ? i have never seen this in my textbook . This is just another notes given by my senior. Homework EquationsThe Attempt at a Solution
  30. gracy

    Formula f=-dU/dx: Non-Conservative Forces

    Is it true that we can't use the formula ##f##= ##\frac{-dU}{dx}## when external source of energy or some external force is present? I think it should rather be "we can't use ##f##= ##\frac{-dU}{dx}## when non conservative force is present" because potential energy is defined only for...
  31. W

    Formula of Forces: 2.1 & 0.35 Meaning

    Homework Statement what is the 2.1 and 0.35 refers to in the equation of (9810)(2.1)(4.2)- 9810(0.35)(0.7) -Fx = 1000(5.88)(8.4-1.401) ?? is it the width ? but , the width is not given ? Homework EquationsThe Attempt at a Solution
  32. J

    Explanation of formula T = 2pi sqrt(m/k)

    Homework Statement This formula we've been using recently, I don't understand where it comes from. Homework Equations T = 2pi * sqrt(m/k) The Attempt at a Solution Hooke's law: F = -kx E(total) = .5mv^2 + .5kx^2 Circumference of a Circle: C = 2 * pi * r I figure these piece together, but I...
  33. W

    Formula of object immersed in water

    Homework Statement why the y ſ P dA will equal to P yc A ? why not P (yc^2) A ? since yc = ſ y dA / A Homework EquationsThe Attempt at a Solution
  34. evinda

    MHB How can we find the formula of the force?

    Hello! (Wave) A force $6N$ forms an angle $\frac{\pi}{4}$ with the y-axis, showing to the right. The force is opposed by the movement of an object along the line that connects $(1,2)$ with $(5,4)$. I want to find a formula for the vector-force $F$. The line that connects $(1,2)$ with $(5,4)$...
  35. I

    Formula using rational numbers

    I want to convert a recursive real formula to rational number representation, but I get the wrong response. For the real formula: k = 1.9903694533443939 u1 = -12.485780609032208 u2 = -6.273096981091879 u3 = k * u2 -u1 /// 1st iteration u3 = -1.7763568394002505E-15 // approx. zero /// 2nd...
  36. W

    Viscosity Formula: Why Not (mass x length)/(time x area)?

    Homework Statement why the alternative formula of viscosity not = (mass x length ) / ( time x area) ? for force x time , we would get (mass x length ) / time ... Homework EquationsThe Attempt at a Solution
  37. A

    Finding acceleration from distance and time

    Homework Statement A bullet with a mass of m=15.5 g is shot out of a rifle that has a length of L=1.02 m. The bullet spends t=0.16 s in the barrel. Write an expression, in terms of given quantities, for the magnitude of the bullet's acceleration, a, as it travels through the rifle's barrel...
  38. M

    How to derive Mersenne's fundamental frequency formula?

    I'm talking about equation 22, Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it. L would be the length, F would be force, and μ would be mass per unit length. f is the frequency Thanks
  39. K

    Deriving the Formula for 2D Motion with Constant Acceleration

    1. Homework Statement how to get R=Vi 2 sin2θ/g y=x*tanθ-[x2*g]/[2(Vi*cosθ)2] Homework Equations Vy=Vi*sinθ-gt y=Vi*sinθ*t-1/2gt^2 Vx=Vi*cosθ x=Vi*cosθ*t The Attempt at a Solution I use this formula to find the expression for t Vy=Vi*sinθ-gt gt=Vi*sinθ t=Vi*sinθ/g I substitute it into...
  40. evinda

    MHB Why Does the Vector Projection Formula Work?

    Hello! (Wave) Given two vectors $a$ and $b$ why does it hold that the vector projection of $a$ on $ b$ is $$\frac{\vec{a} \cdot \vec{b}}{||\vec{b}||^2} \cdot \vec{b}$$ ? Could you explain to me why the formula holds?
  41. J

    I Deriving the Lorentz formula from my own example

    Good day to you all, I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...
  42. I

    How Does Cauchy's Theorem Support Complex Integral Formulas?

    Homework Statement Verify that a) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}\bar z}{1-\bar z e^{it}}dt = 0##, if ##f(w)## is analytic for ##|w|<1+\epsilon##, and that b) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}}{e^{it}-z}dt = f(z).## for ##z = re^{i\theta}## with ##r <...
  43. Gwyndolin

    How to derive formula for nucleus decay using this equation?

    Homework Statement The formula being derived is N=No*e^k*t, from the equation Nn=No/2^n where No is the initial number of particles and the lowercase n in the second equation is the number of half lives. The n in Nn just indicates the number of particles after so many half lives. You might also...
  44. D

    The Mysteries of De Moivres Theorem and Euler's Formula

    Homework Statement 2. Homework Equations [/B] De Moivres Theorem/ Eulers formula The Attempt at a Solution Honestly don't know where to go with this now. I already applied De Moivres theorem at the very end. It feels like I have to do something more with either De Moivres theorem or...
  45. teroenza

    Breit-Rabi Formula Derivation for j=1/2

    Homework Statement Derive the Breit-Rabi equation in the case that the quantum number j is equal to 1/2, specifically the 1S_1/2 state of Hydrogen. This is the equation describing hyper-fine and Zeeman splitting of the energy levels in an applied magnetic field. Homework Equations We are given...
  46. T

    Finite geometric series formula derivation? why r*S?

    what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure
  47. P

    Euler Formula: Understanding (4.25) to (4.26)

    can someone explain how you go from (4.25) to (4.26) using Euler's formulas in the attachment?
  48. Greg Bernhardt

    Can a Formula 1 Car Outperform a Rugby Scrum in a Race?

    Not saying this is fake, but it seems pretty incredible to me. Can anyone shine some light on this?
  49. W

    Head Loss Formula: Gamma Meaning Explained

    Homework Statement what does the gamma in the formula mean ? since the other terms in the formula are the same , i can just cancel it, leaving μ / γ = v /g . So , γ has unit of kg(m^-2)(s^-2) ? Homework EquationsThe Attempt at a Solution
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