Constants Definition and 486 Threads

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.
There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and its dimension is length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.
The term fundamental physical constant is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above. Increasingly, however, physicists only use fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α.
Physical constant, as discussed here, should not be confused with other quantities called "constants", which are assumed to be constant in a given context without being fundamental, such as the "time constant" characteristic of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity).
Since May 2019, all of the SI base units have been defined in terms of physical constants. As a result, five constants: the speed of light in vacuum, c; the Planck constant, h; the elementary charge, e; the Avogadro constant, NA; and the Boltzmann constant, kB, have known exact numerical values when expressed in SI units. The first three of these constants are fundamental constants, whereas NA and kB are of a technical nature only: they do not describe any property of the universe, but instead only give a proportionality factor for defining the units used with large numbers of atomic-scale entities.

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  1. P

    Rate of reaction, rate constants, and Arrhenius' Equation

    Homework Statement The effect of temperature on the rate of a reaction was studied and the following data obtained: k (s-1) T (°C) 3.06×10-4 10 4.84×10-4 16 6.50×10-4 20 1.40×10-3 31 2.87×10-3 42 4.16×10-3 48 5.94×10-3 54 7.92×10-3 59 It is known that...
  2. Z

    Inequality with negative constants

    Homework Statement Solve each of the following inequalities; give your answers in interval notation. i) ax + b < c, where a, b, c are negative constants Homework Equations The Attempt at a Solution ax < c - b x > c - b / a because I'm dividing by a negative constant...
  3. S

    Finding Spring Constants After Cutting a Spring

    Homework Statement A spring with spring constant 8 N m-1 is cut into 2 equal parts. Find the spring constant of each part? Homework Equations The Attempt at a Solution Spring constant of each part = 16 N m-1 Above is the answer given. 1. Why should we times 2? 2. If the...
  4. K

    General solution to PDEs-arbitrary constants

    Homework Statement Claim: For the partial differential equation ∂u/∂x + ∂u/∂y = 0, the general solution is u(x,y) = f(x-y) Homework Equations N/A The Attempt at a Solution I remember that the number of arbitrary constants in the general solution should be the same as the order of the...
  5. R

    The shape of space-time and physical constants

    I am wondering if anyone knows of research being done, or theories that are related to the actual structure of space-time as they are related to physical constants such as the speed of light, Planck's constant, and the cosmological constant. I'm far from being a expert, but I've been playing...
  6. R

    Which are the constants needed for the universe to exist?

    I heard a http://www.youtube.com/watch?v=YtdE662eY_M"by Brian Greene where he states that there are over 20 constants needed for the universe to exist, Which are those constants?
  7. S

    Can Spring Constants Be Negative?

    Homework Statement can spring constants ever be negative??
  8. U

    Does + C melt together ALL constants?

    Does "+ C" melt together ALL constants? I had this integral \int \frac{dy}{-2y + 6}. I realize you can let u = -2y + 6 so that du = -2dy, and adjusting: -0.5 du = dy. The integral becomes -0.5 \int \frac{du}{u} = -0.5 \ln{|-2y + 6|} + C However, there is another way. Factor out the...
  9. D

    Solving Spring Constants with 7.50-kg Ball & 2 Springs

    Homework Statement A 7.50-kg ball is placed on top of a spring with a spring constant of 475 N/m that has an initial length of 35.0 cm (h1). When the ball has reached its equilibrium position, it is supported by both springs at a height of 20.0 cm above the table (h3). If the shorter spring...
  10. H

    Understanding H NMR Coupling Constants: Matching J-Values vs. Peak Alignment

    background: I have a HNMR spectra and I am trying to figure out what is coupled to what. There is a set of 4 doublets where it is know that there 2 sets of coupled doublets. the doublets have j-values of 8.8 @ 8.04ppm, 8.8@ 7.58ppm, 8.4@7.39ppm and 8.4@7.00ppm. While I may have assumed that...
  11. D

    Calculating Gravitational Field Constants for Mars, Jupiter, and Mercury

    1. Calculate the gravitational field constants for the following: Mars (r=3.43 x 10^6m , m= 6.37 x 10^23 kg) Jupiter (r= 7.18 x 10^7 , m = 1.90 x 10^27kg) Mercury (r=2.57 x 10^6m , m= 3.28 x 10^23 kg) 2. F = mg Fg = Gm1m2 r^2 3. So i tried subbing these given masses into the second...
  12. J

    Structure constants of a group antisymmetric?

    First, how do you put in spaces without them being deleted when i post? How does one show that the structure constants, c^{k}_{ij} of a group are antisymmetric? The context is from page 12 of Anderson's "Principles of Relativity Physics", with the statement right at the bottom: Thanks for...
  13. G

    Constants in a system of equations that makes the system consistent

    Homework Statement The Attempt at a Solution For a) I just solved simultaneous equations, a link to a resource that solves a system more efficiently would be nice but augmented matrices are taught in the syllabus, or atleast not in the official text. Although I've seen solutions in...
  14. W

    Parameters, Arguments, Variables, Constants I`m confused,

    First of all, I understand what a constant is, what a variable is, and somewhat what a Parameter is. For parameters, as much as I know they are variables but of a specific type, for exmaple:- a^2= B, where B is the area of the square..now "a" is a variable, but its also a parameter, since...
  15. I

    Λa+µb+vc =0 constants not all zero c.(axb)=0

    Homework Statement past paper qu... λa + µb + vc = 0 for some λ, µ, v not all zero show c.(axb)=0 consider cases v not equal to 0 and v = 0 The Attempt at a Solution not sure how to start so if someone could just point me in the right direction or offer another hint it may help me get...
  16. N

    Measuring the magnetic and electric constants

    Has the permeability and permittivity of vacuum ever been measured in a vacuum or space?
  17. F

    Calculating RC & LC Time Constants: Series vs. Parallel

    How does the relative position(series or parallel) of a resistor affect the calculation of the RC and LC time constants. In other words is a RC time constant still R\timesC requardless of whether or not R and C are parallel or if R and C are in series. Same question with LC time constants, is...
  18. B

    Calculating Constants for Conservative Vector Field F

    We are told that the force field F=(\muz + y -x)i + (x-\lambdaz)j + (z+(\lambda-2)y - \mux)k Having already calculated in the previous parts of the question 1:the line integral (F.dx) along the straight line from (0,0,0) to (1,1,1) 2:the line integral (F.dx) along the path x(t)=(t,t,t^2)...
  19. D

    Dielectric constants of polymeric materials

    I have done a series of tests on the dielectric constant of polymeric materials using Impedance measurements in a four electrode configuration. When varying the thickness of my polymeric materials, the dielectric constant remains relatively "constant". When the thickness of the material is...
  20. C

    Unwanted constants after integration

    While integrating a rational function I stumbled upon the following problem (In the calculation of the integral the substitution u=x+1, du=d(x+1)=dx was used). \begin{align} \int \frac{x^2}{(1+x)^2}\,dx &= \int \frac{(u-1)^2}{u^2}\,du \\ &= \int du+\int \frac{du}{u^2}\ -2 \int...
  21. Y

    Where i can find complete data for material elastic constants?

    Where i can find complete data for material elastic constants?? I need elastic constants, piezoelectric coefficients & permittivity for different semiconductor alloy? Someone could kindly help...
  22. E

    Finding the constants of a function

    Homework Statement Suppose f(x)=ax^3+bx^2+cx+d has stationary points at (1,3) and (3,-3). Find the constants, a, b, c, d and sketch the graph of f(x). Homework Equations The Attempt at a Solution No idea where to start with this one. I know I have to eliminate 3 of the variables...
  23. Y

    Understanding Equilibrium Constants With No Denominator

    Lets say you have something like CaSO4 (s) <-----> Ca (aq) + SO4(aq) The equilibrium constant would then have no denominator. That makes no sense to me! K would equal [ Ca ][ SO4 ]. Wouldn't that then represent a constant amount of moles no matter how much CaSO4 is present...
  24. C

    What is the effect of arranging two springs in series?

    I have two springs arranged in series (remember circuit diagrams from physics class!). One has a low stiffness constant (K1 = 5) and the other connected to it has a much higher contant (K2 = 100). According to the equation (as used in wikipedia)...
  25. P

    Rate Constants From Equilibrium Constants

    Hi, I am currently attempting to implement the Gillespie algorithm for an artificial gene network. I have been given a set reactions and their accompanying equilibrium constants. However, to execute the algorithm I must know the rate constant of the reaction (units of 1/s). I know that the...
  26. P

    Universal Constants: Books for Laymen about Observable Effects

    Are there any books, written for the layman, which talk about observable effects that might be caused by our 5 (4 + time) dimensional portion of the universe moving through the larger universe. "Universe in a Nutshell" -Hawking, talks about how gravity may transend branes. Are there others?
  27. S

    Why Can't I Get the Correct Constants in My Chemical Reaction Calculations?

    Homework Statement This is an example from a book. I am having trouble in substituting the numbers to get the given result. Homework Equations The bar notation is to indicate the operating point. The subscript A is for the reactant A (which reacts and becomes product B in a A->B...
  28. C

    How to Find the Area Under y = cos(x) Above y = k?

    Homework Statement Let A be the area of the region in the first quadrant under the graph of y = cos (x) and above the line y = k for 0 <= k <= 1. a.) Determine A in terms of k. b) Determine the value of A when k = 1/2. c) If the line y = k is moving upward at the rate of ( 1 / pi )...
  29. A

    Help With Spring Constants and Oscillaions

    Homework Statement A toy car with mass 0.02 kg is propelled by a spring with a spring constant 80 N/m onto a track. The track. The track contains a loop of radius 0.10m. Ignore any losses dueto friction and use g=10m/s. What is the minimum compression of the spring necessary for the car...
  30. KleZMeR

    Dsolve: assigning constants of integration and subscripts

    I have an equation I am solving with Mathematica: In: DSolve[y''[t] + Subscript[\[Omega], c]^2 y[ t] == -Subscript[\[Omega], c]^2 Subscript[v, d]*t + Subscript[\[Omega], c]*Subscript[v, 0], y[t], t] Out: {{y[t] -> C[2] Cos[t Subscript[\[Omega], c]] + C[1]...
  31. J

    What are the normalizations constants of psi(x) in a finite potential box?

    What are the normalizations constants of psi(x) in a finite potential box? is there an algebraic or analytical solution. I have the solution to the infinite box but it seems the two cases are not comparable. As in the finite box the particle does not need to be in the box?
  32. B

    Is My Lie Algebra 4D or 5D Given These Structure Constants?

    I have five generators of a lie algebra, g_1,g_2,g_3,g_4,g_5 which at first glance I believe are independent, although I could be wrong. I have calculated the structure constants, i.e. \left[g_i,g_j\right]=f_{ij}^k g_k And from that I have calculated a matrix rep using...
  33. C

    Can Oxygen Radicals Be Directed to Chlorine Monoxides to Form Oxygen Gas?

    from where do chlorine monoxides form? I'm asking this because I'm just wondering if there is a way to direct all the oxygen radicals on its way to react with ozone to a whole bunch of chlorine monoxides to form oxygen gas. Is that possible or what? I'm a guy who likes to teach.
  34. A

    Finding Constants for a Gaussian PDF

    Homework Statement The exam grades in a certain class have a Gaussian PDF with mean m and standard deviation \sigma. Find the constants a and b so that the random variable y=aX+b has a Gaussian PDF with mead m' and standard deviation \sigma'. Homework Equations The Attempt at a...
  35. S

    Calculating decay constants and half-life

    A scientist wishes to find the age of a sample of rock. Realising that it contains radioactive potassium, which decays to give a stable form of argon, the scientist started by making the following measurments: decay rate of the potassium in the sample = 0.16Bq mass of potassium in the sample...
  36. U

    Finding pH using acidity/basicity constants

    technically it is not homework, more like struggling with textbook material, but something tells me it would end up here anyway so here it is : there's something about the method that gives me different results using different paths so I'm going to show both of them and see if you can spot the...
  37. J

    How Does Friction Affect Spring Compression and Block Displacement?

    Two identical massless springs of constant k = 200 N/m are fixed at opposite ends of a level track, as shown in Figure P5.62. A 5.90 kg block is pressed against the left spring, compressing it by 0.150 m. The block (initially at rest) is then released, as shown in Figure P5.62a. The entire track...
  38. P

    Universal constants changing into new ones?

    Just a quick question: the transition between pre-big bang to post big bang (if it occured) required a change in physical constants (our universe is ever-expanding while the preBB universe was not). How can these constants change themsevels into new constants like that? This would seem to...
  39. L

    How to Calculate Structure Constants of SU(N) Using Kroenecker Deltas?

    Hi there, Does anybody know how to exploit the product of structure constants of SU(N) through Kroenecker deltas? I mean \sum_a f_{abc}f_{ade} I know this for SU(2) as in this case I have the Levi-Civita symbol but in other cases I was not able to recover it in literature. Any...
  40. A

    How to find two constants in an equation

    Homework Statement i'm trying to find two constants in the same equation. its an initial value problem there's a two parameter family x=c1cost+c2sint with initial conditions x''+x=0, x(pi/6)=1/2, and x'(pi/6)=0 so I'm trying to find c1, and i equate the problem to 1/2 and subsitute...
  41. A

    Temperature Dependence of Dielectric Constants

    Does anyone have information on temperature dependence of dielectric constants? I haven't been able to find anything general enough on Google. I'm particularly interested in Polyethylene, Teflon, and Air but a general description would also be appreciated.
  42. A

    How Do You Calculate the Constants A and C for a Rocket's Trajectory Equation?

    A rocket is fired at an angle from the top of a tower of height 50.0m. Because of the designs of its engines, its position coordinates are of the form x(t)=A+Bt^2 and y(t)=C+Dt^3, where A, B, C, and D are constants. The acceleration of the rocket after 1.00s after firing is a=...
  43. I

    Finding the constants in a Sine equation.

    Homework Statement I have been puzzling over this question for hours now. The centre of a wall clock is 180 cm above the floor. The hand of the clock that indicates the seconds is 20 cm long. The height, h cm above the floor, of the tip of the second hand, t seconds after midday, is...
  44. C

    Structure constants of su(2) and so(3)

    SU(2) and SO(3) "have the same Lie algebra". While I understand that their corresponding lie algebras su(3) and so(2) have the same commutator relations \mbox{SO(3)}: \left[ \tau^i, \tau^j\right] = \iota \varepsilon_{ijk} \tau^k \mbox{SU(2)}: \left[ \frac{\sigma^i}{2}...
  45. N

    Question about fine-structure and free vacuum constants

    Hello, When the fine structure constant (a) is calculated from the electric and magnetic constants. What does each part represent. (1/c) * (1/electric_constant) * (e^2/(2*h)) = a i.e. What does (1/electric_constant) represent? The opposite of vacuum permittivity?And with the...
  46. T

    Hooke's Law: inconsistent spring constants what

    Homework Statement A 70 kg bungee jumper leaps off a bridge. She is tied to a 12 m long bungee cord and falls a total of 31 m. Calculate: a) the spring constant of the bungee b) the maximum acceleration experience by the jumper Homework Equations F = kx Eg = Ee where g is...
  47. H

    How constant are constants? - ice skating

    I recently read a thread that pointed to some constants that caught my attention. Before I go off the deep end with a question it would seem to be a good idea to understand exactly how constant are certain constants. I'm specifically curious as to the constants of: Length of a day (sidereal...
  48. R

    Pauli Matrices and Structure Constants

    Hey folks, I am trying to generate the Pauli matrices and am using the following formula taken from http://en.wikipedia.org/wiki/SU(3 ) "In the adjoint representation the generators are represented by (n^2-1)×(n^2-1) matrices whose elements are defined by the structure constants"...
  49. B

    Find constants and antiderivative problem

    Homework Statement Find constants c1 and c2 such that F(x) = c1xsinx+c2cosx is an antiderivative of f(x) = 4xcos(x)+3sin(x) Homework Equations d/dx cosx = -sinx d/dx sinx = cosx The Attempt at a Solution Don't know how to setup or handle a problem such as this. Prolly much simplier...
  50. Y

    Understanding Equilibrium Constants 0 & 1

    Hi, can someone help me on the following question. Equilibrium constant=0 Equilibrium constant=1 What are the significance of these 2 values? As in, what is happening to the reactants as well as the products in this 2 instances? Thank you!
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