What is quantities: Definition and 207 Discussions

Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.
Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others function as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little.
Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: matter, mass, energy, liquid, material—all cases of non-collective nouns.
Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios.

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  1. D

    How might I liquefy small quantities of natural gas?

    Several undergraduate and graduate students and I are building a small engine powered by Compressed Natural Gas (CNG). It is a small and straightforward affair, similar to what is found in small equipment such as chainsaws and lawn mowers. I wanted to experiment with Liquefied Natural Gas (LNG)...
  2. T

    I Scalar quantities and complex numbers

    I was taught a scalar is a quantity that consists of a number (positive or negative) and it might include a measuring unit, e.g. 6, 5 kg, -900 J, etc. I was wondering if complex numbers like 3 + 7j (where j is the square root of minus 1) can be considered scalar quantities too, or is it that...
  3. StarWarsNerd

    B Calculating Linear and Angular Quantities from Applied Force

    In the image above, a centroid with radius 1 is depicted. F1 is pointing directly at point A (which is the center of the circle), and F2 is pointing directly at point B. The radius for finding the torque would be the perpendicular between the center of the object and the force vector, so r1...
  4. C

    I Cartesian and polar quantities

    Hi, I have a little doubt. I have, referred to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values). I can easely calculate the polar coordinates (longitude and latitude - along with distance). My doubt is: how do I calculate the longitude and...
  5. A

    B Why physical quantities need a unit?

    my question is why physical quantities need a unit?
  6. Z

    Ratio Question with 3 quantities

    Homework Statement If 15 workers can pave 18 driveways in 24 days, how many days would it take 40 workers to pave 22 driveways Homework Equations Actually i don't know which equation should be used for 3 quantities. I know the eq for two quantities. Because we increasing labours so we would...
  7. F

    B Explaining vector & scalar quantities to a layman

    I've been asked by someone with minimal background in physics to explain what vector and scalar quantities are and give examples. Here are my thoughts: A scalar is a quantity that has a magnitude only, it is completely specified by a single number. Importantly, it has no directional dependence...
  8. P

    B Exploring the Meaning of "d" in Differential Physical Quantities

    [Mentor's note: This question was split off from: https://www.physicsforums.com/threads/meaning-of-physical-quantities-and-division.880214/] What does this differential "d" mean? Why say dE instead of E? or
  9. P

    B Meaning of physical quantities and division

    I read this interesting thread trying to find an answer to my questions (and I got even more confused). I study radiometry units in context of computer graphics. I have a few questions, starting from the basic ones: 1. Following AlexS's note, why is speed=distance/time and not distance*time? 2...
  10. J

    Engineering Finding Unknown quantities in a circuit

    Homework Statement See attached photo Homework Equations Kirchhoff's current law[/B] The Attempt at a Solution So, I was solving for I3 and got the correct answer, but I want to be sure that I arrived at the right answer by using a reliable thought process. I don't want to get lucky! So...
  11. Y

    Prove mass, velocity and KE are their respected quantities

    I have done the example for momentum. And I gather that scalar*vector=vector. I know that mass and KE is scalar, velocity is vector. Can someone show me proofs like for what I have said above. Not just mass is scalar because it does not have direction etc. Thank you.
  12. G

    'Physics' Terms for Integral quantities?

    'Flux' is often used to describe quantities associated with a surface integral. I wonder if there are corresponding terms for the line and volume integrals. Linflux? Volux?
  13. A

    Conserved quantities for massless particles (Schwarzschild)

    If a metric admits a Killing vector field ##V ## it is possible to define conserved quantities: ## V^{\mu} u_{\mu}=const## where ## u^{\mu}## is the 4 velocity of a particle. For example, Schwarzschild metric admits a timelike Killing vector field. This means that the quantity ##g_{\mu 0}...
  14. H

    Are all physical quantities an equivalence relation?

    Consider this self-evident proposition: "If object A has the same mass as object B and object C separately, then object B has the same mass as object C." Why isn't this stated as a law, but the zeroth law of thermodynamics is? Is there a physical quantity u such that the u of A is equal to the...
  15. evinda

    MHB Why are the quantities equal to 0?

    Hello! (Wave) I am looking at the general form of the Simplex algorithm with the use of tableaux. $\overline{x_0}$ is a basic non degenarate feasible solution and thus the columns $P_1, \dots, P_m$ are linearly independent. The first step is to create a $(m+1) \times (n+4)$ matrix as follows...
  16. F

    Chain rule and Kinematic quantities x,v,a

    Hello Forum, I have a couple of kinematics questions. The position of a point object is given by the position vector x(t). Speed is v(t)=dx(t)/dt and the acceleration a(t)= dv(t)/dt. What if we wanted to know the velocity and/or the acceleration as a function of position, i.e v(x) or a(x)...
  17. EnigmaticField

    The relation between Lie algebra and conservative quantities

    In quantum mechanics, a physical quantity is expressed as an operator G, then the unitary transformation coresponding to the physical quantity is expressed as exp(-iG/ħt), being also an operator, where t is the tranformation parameter. G is actually the conservative quantity corresponding to the...
  18. F

    Finding some quantities of particles moving relativistically

    Homework Statement A 2.5 MeV photon is moving in positive x-direction and an electron in the opposite direction at a velocity of 0.99c. Calculate their common total energy, momentum and total rest mass.Homework Equations Relativistic EquationsThe Attempt at a Solution I have some concerns...
  19. KostasV

    Conservative physical quantities

    Hello ppl ! If i find that a physical quantity (lets say angular momentum operator vector L) is conservative (this means [H,L]=0 - H=hamiltonian ) then its 3 components Lx , Ly and Lz are being conserved too ? That happens with every conservative vector operator ? Like spin vector S and his...
  20. C

    Noether's theorem and constructing conserved quantities

    Homework Statement A particle of mass m and charge e moving in a constant magnetic field B which points in the z-direction has Lagrangian ##L = (1/2) m( \dot{x}^2 + \dot{y}^2 + \dot{z}^2 ) + (eB/2c)(x\dot{y} − y\dot{x}). ## Show that the system is invariant under spatial displacement (in any...
  21. evinda

    MHB Which quantities do we use?

    Hello! (Wave) A thin cover with the shape of a rectangle with mass per unit of volume equal to $m_f$ is put over a quantity of explosive ( with mass per unit of volume equal to $m_e$), that is attached at a base of a practically unbounded mass. If the explosive explodes, the cover is getting...
  22. ZARATHUSTRA

    Surface integral for scalar quantities

    so for surface integral for scalar quantities. Why do we use cross product not dot product in the integral? but can we just add an unit normal vector n to make the direction the same? My question seems really stupid too a lot people, but this is really my confusion to surface integral. please...
  23. S

    Identifying conserved quantities using Noether's theorem

    I've been asked to find the conserved quantities of the following potentials: i) U(r) = U(x^2), ii) U(r) = U(x^2 + y^2) and iii) U(r) = U(x^2 + y^2 + z^2). For the first one, there is no time dependence or dependence on the y or z coordinate therefore energy is conserved and linear momentum in...
  24. C

    Conserved quantities in the cart and pendulum problem

    A problem on an assignment I'm doing deals with a cart of mass m1 which can slide frictionlessly along the x-axis. Suspended from the cart by a string of length l is a mass m2, which is constrained to move in the x-y plane. The angle between the pendulum and vertical is notated as phi. The...
  25. S

    Connections between Linear and Rotational Quantities

    Homework Statement A wheel of radius R starts from rest and accelerates with a constant angular acceleration α about a fixed axis. At what time t will the centripetal and tangential acceleration of a point on the rim have the same magnitude? Homework Equations acp=r x ω2 at= r x α ω= 2π / T...
  26. S

    Graph of gravitational quantities against distance

    I want to ask the graph of gravitational force against r and gravitational potential energy against r. First, about gravitational force against r The shape of the graph is straight line from origin until the surface of the sphere and then curve (decreasing). I understand about the decreasing...
  27. cseil

    Local and integral physical quantities

    Hello everyone, I'd like to know if my understanding of local and integral quantities is clear. An integral quantity refers to the entire physical system, it is not defined point by point. A local one is defined point by point, for example ρ(x,y,z). Can I consider the charge dq as a local...
  28. Anique

    Dimensions of physical quantities

    Hello there, I have a confusion between dimensions and units! All of others tell me its not unit but some use units! Please verify the following Quantity Dimension Length L Mass M Time T Temperature Θ Amount of...
  29. B

    How to get the conserved quantities of a integrable quantum system?

    If I have an arbitrary quantum many-body model, what is the method to calculate the the conserved quantities if the model is integrable. If it is hard to explain, can you recommend some relevant books for me? Thanks a lot!
  30. KleZMeR

    Invariant quantities of a lagrangian?

    Given a basic Lagrangian, how would I determine invariant quantities? My hunch says it would be quantities that do not depend on position or time? Saying that, perhaps using the Lagrange equation to solve for equations of motion and along the way whatever terms disappear would be my invariant...
  31. J

    Finding Conserved Quantities for Analytical Mechanics Exam Questions

    Hi all, I am preparing for my "second chance exam" in analytical mechanics. It is a graduate course i.e. based on geometry. (Our course notes are roughly based on Arnold's book). I was able to find some old exam questions and one of those has me stumped, completely. The question gives 3...
  32. M

    Thermodynamic state entirely determined by only two quantities?

    I am trying to understand why I can specify the specific volume v of a fluid element as a function of the equilibrium pressure, p, and the equilibrium entropy, s. This is for example done in this article http://www.sno.phy.queensu.ca/sno/str/SNO-STR-95-051.pdf , on this website...
  33. C

    Index gymnastics of electromagnetism quantities

    This bothers me, and the question is simple: If am working with a non-minkowski metric g, when raising or lowering indexes of electromagnetism quantities, for example the electromagnetic tensor F, or the vector potential A, should I use my curved spacetime metric g or the minkowski metric n?
  34. kelvin490

    Question about thermodynamic quantities

    We know that for constant pressure thermodynamic processes, dH=dqp. My question is, does it implies that only reversible work is possible in this processes so that dw=0 because dv is zero? In addition, does qv necessarily be reversible heat transfer in this case? What if the heat transfer is...
  35. M

    Determining quantities as vectors or not

    Why are some quantities vectors while others aren't? For example, we can calculate both current and current density, but why do we only consider current density to be a vector and current a scalar quantity? Is it a purely arbitrary convention or is it something more mathematically fundamental? I...
  36. T

    Trajectories with Conserved Quantities

    Homework Statement A particle moves along a trajectory with constant magnitude of the velocity |\stackrel{→}{v}|=\stackrel{→}{v0} and constant angular momentum L⃗ = L⃗0. Determine the possible trajectories. Homework Equations d(L⃗)/(dt)=\stackrel{→}{N} where \stackrel{→}{N}=torque...
  37. ShayanJ

    Newton's expansion for non-commutative quantities

    You probably know that for two commutative quantities x and y,we have: (x+y)^n=\sum_{r=0}^n \left( \begin{array}{c} n \\ r \end{array} \right) x^{n-r} y^r Now I want to know is there a similar formula for the case when x and y don't commute and we have [x,y]=c and [x,c]=[y,c]=0 ? Thanks
  38. T

    Which Unit Is Not a Basic Quantity in Mechanics?

    Homework Statement All the following are units of basic quantities except ______. Select one: a. second b. slug c. kilogram d. meter e. pound Homework Equations The Attempt at a Solution i have eliminated the answers a, c,d i now the answer is between pound and a slug on...
  39. paulmdrdo1

    Word problems: mathematical descriptions of stated quantities

    1. a.if john finished the job in 8 days, what was the part he finished in n days? b. by how much 4k greater than 4h? c. represent the amount of salt in x gallons of a 25% by volume of salt in solution water. d. represent 3 consecutive integers if the smallest is n. answers a. n/8 b. 4h+4k c. i...
  40. J

    Calculating Uncertainties of Measured quantities (Physics)

    Homework Statement d1 = 2.53 cm +/- .05 cm d2 = 1.753 m +/- .001 m 0 = 23.5 degrees +/- .5 degrees v1 = 1.55 m/s +/- .15 m/s Using the measured quantities above, calculate the following. Express the uncertainty calculated value. Homework Equations d3 = 4 ( d1 + d2) The...
  41. J

    MHB Calculating Uncertainties of Measured quantities (Physics)

    d1 = 2.53 cm +/- .05 cm d2 = 1.753 m +/- .001 m 0 = 23.5 degrees +/- .5 degrees v1 = 1.55 m/s +/- .15 m/s Using the measured quantities above, calculate the following. Express the uncertainty calculated value. a = 4 v1^2 / d2 a = 4 (1.55 m/s +/-.15 m/s)^2 / 1.753 m +/- .001 m a = 6.8 m/s...
  42. C

    Two-level quantum system observable quantities

    Homework Statement A two-level system is spanned by the orthonormal basis states |a_{1}> and |a_{2}> . The operators representing two particular observable quantities A and B are: \hat{A} = α(|a_{1}> <a_{1}| - |a_{2}> <a_{2}|) and \hat{B} = β(|a_{1}> <a_{2}| + |a_{2}> <a_{1}|) a) The state...
  43. T

    Why Hot Water in Smaller Quantities is Less Painful

    When tiny droplets of hot water touch your hand you don't feel much pain but when large amount of hot water spills on your hand it will cause serious injuries. Why? - is this due to the heat energy in the tiny droplets of water is lesser so the energy transferred to the hand is lesser...
  44. T

    Calculating masses of unknown quantities of reactants.

    Homework Statement Calculate the number of moles and mass of BaCl2 and NaCl in the original mixture. Homework Equations We prepared a solution of 0.35M Na2SO4. We then obtained an unknown mixture of BaCl2•2H2O and NaCl, weighed 1 g and added it to 200 mL of water and 10 mL HCl. Finally we...
  45. C

    Conserved quantities as symmetry generators

    Suppose we have a Lagrangian \mathcal{L(\phi, \partial_\mu \phi)} over a field \phi, and some variation on the field \delta \phi. If this variation induces a variation \delta \mathcal{L} = \partial_\mu F^\mu for some function F^\mu, then Noether's Theorem tells us that if we construct the...
  46. J

    Can continuously (strongly) measured quantities ever change state?

    Alan Turing made the following claim: "It is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be...
  47. F

    Showing the expectation values of a system are real quantities

    Homework Statement A one-dimension system is in a state described by the normalisable wave function Ψ(x,t) i.e. Ψ → 0 for x → ±∞. (a) Show that the expectation value of the position ⟨x⟩ is a real quantity. [1] (b) Show that the expectation value of the momentum in the x-direction ⟨p⟩...
  48. W

    Physical quantities versus wave function?

    hi, please explain can by using suitable operator we can find any physical quantity- as by using hamiltonian on wave function we can find energies by the eigenvalues? thanks wasi-uz-zaman
  49. D

    How to spot conserved quantities from Lagrangians

    Hi guys, The title pretty much says it. Say you have a very simple 3D Lagrangian: L = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2 + \dot{z}^2) - V So How do you tell what is conserved from a generic potential? I know for example that if V = V(x,y,z) then the total linear momentum is not...
  50. A

    Are properties quantities or do properties have quantities?

    The title pretty much says it all, but let me elaborate on the source of confusion. VIM defines quantity as: Other definitions I found are extremely circular. They typically go like this, "a physical quantity is a property that can be quantified". In other words, they explain quantity with...
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