What is deriving: Definition and 1000 Discussions

SI derived units are units of measurement derived from the
seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities.
The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density.
The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m".

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  1. S

    Deriving equation 9.91 in Carroll's Book "Spacetime and Geometry"

    Hello dear PhysicsForums attendees! I tried to solve for somebody the aforementioned problem. But I am not sure if my attempt is correct. So I am writing down what I suggested. Looking at eq 2.46 in Carrolls book; The metric is Lorentzian in General Relativity so that ##g^{\mu \nu} =...
  2. R

    Deriving the Law of Reflection from Huygens Principle

    Attached is section 33.7 from my book, which introduces Huygen's principle in order to derive the law of reflection. I am more used to the ray model rather than the wave model, so I'm constantly going to try to relate everything back to rays. Making this connection also helps with completeness...
  3. snoopies622

    I Derive Escape Velocity GR: Source for Schwarzschild Metric

    I was surprised to read that the formula for escape velocity — at least for a spherical mass like the Earth — is the same in relativity as it is in classical physics: v_e = (2GM/r)^{1/2} I'm wondering if someone can give me a good source for deriving this. (I assume one takes a radial...
  4. S

    Deriving relations for a hard sphere phase diagram

    Ornstein-Zernike states that ##h(r_{12}) = c(r_{12}) + \rho \int d\mathbf{r}_3 c(r_{13})h(r_{32})## which after a Fourier transform becomes ##\hat{C} (\mathbf{k}) = \frac{\hat{H}(\mathbf{k})}{1+\rho \hat{H}(\mathbf{k})}## However, I don't see how to simplify this to the second equation he has...
  5. thaiqi

    Deriving Statistical Behavior of Particles via Classical Mechanics

    Hello, using computation simulation, can the statistical behavior of many particles be derived through deterministic classical mechanics?
  6. J

    I Deriving vacuum FRW equations directly from action

    Using the Einstein-Hilbert action for a Universe with just the cosmological constant ##\Lambda##: $$S=\int\Big[\frac{R}{2}-\Lambda\Big]\sqrt{-g}\ d^4x$$ I would like to derive the equations of motion: $$\Big(\frac{\dot a}{a}\Big)^2+\frac{k}{a^2}=\frac{\Lambda}{3}\tag{1}$$ $$2\frac{\ddot...
  7. U

    I Length Contraction & Time Dilation: Proving It

    I have been able to prove to myself that, based on Einstein's two postulates and the the Pythagorean theorem, that time dilates. From here how do I prove that length contracts? (All of this observing a frame that is moving relative to the proper frame at uniform velocity.)
  8. cwill53

    Using the solid angle to simplify an integral when deriving Gauss' Law

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  9. EchoRush

    Help with deriving the formula for kinetic energy (using calculus)

    Hello, I am learning how to use calculus to derive the formula for kinetic energy now, I understandthe majority of the steps in how to do this, however, there is one step where I get totally lost, I will post a picture of the steps and I will circle the part where I get lost. If you see the...
  10. sbrothy

    C/C++ Deriving from C++ STL classes?

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  11. M

    Deriving the 1-D Linear Convection Equation

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  12. S

    B Deriving Lorentz Transformations with 3 Postulates

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  13. S

    I Where did I go wrong in deriving quantized energy?

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  14. Philip Koeck

    Deriving vdW-equation from kinetic theory

    Does anybody know of a derivation of the van der Waals equation from the molecular kinetic theory of gases, but without using the tools of statistical physics (such as partition functions)?
  15. Tony Hau

    I Deriving the differential equation for the underdamped case

    The formula for general oscillation is: The formula for underdamping oscillation is: where λ = -γ +- sqart(γ^2 - ω^2), whereas A+ and A- , as well as λ+ and λ-, are complex conjugates of each other. After some operations, we get: x(t) = Ae^(-γx)[e^i(θ+ωx) +e^-i(θ+ωx)], where A is the modulus...
  16. stephenklein

    Deriving the Relativistic Transverse Doppler Effect (Circular Motion)

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  17. F

    Deriving the Adjoint / Tangent Linear Model for Nonlinear PDE

    I am trying to derive the adjoint / tangent linear model matrix for this partial differential equation, but cannot follow the book's steps as I do not know the math. This technique will be used to solve another homework question. Rather than posting the homework question, I would like to...
  18. weningth

    A Deriving the Callan-Gross Relation via the Parton Model

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  19. E

    Deriving the electrostatic pressure of a water droplet

    I assumed a uniform distribution of charge within the droplet such that ##E = \frac{q}{4\pi\epsilon_{0}r^{2}}## at the outside surface. I then said that the pressure acting at the surface would be the force on a charge element ##dq## within an area ##dA## on the surface, divided by the area...
  20. J

    I Deriving the 4-momentum of a free particle moving in curved spacetime

    Consider a free particle with rest mass ##m## moving along a geodesic in some curved spacetime with metric ##g_{\mu\nu}##: $$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda$$...
  21. currently

    Deriving ground state electron energy using Boundary Value

    This is the equation given. I attempted to use Radial Equation, obtained from separating variables, to solve for ##E_1##.
  22. currently

    Deriving the first-order system for this governing equation

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  23. T

    Deriving Momentum From Newton's Second Law of Motion

    Hello everyone I was hoping someone could shed some light on the following:- I am trying to derive the equation of Momentum from Newton's 2nd Law. What I know is the following:- I don't know how to get from Force = Mass * Acceleration TO Momentum = Mass * Velocity. I have attempted to...
  24. Arman777

    Deriving an identity using Einstein's summation notation

    I have an identity $$\vec{\nabla} \times (\frac{\vec{m} \times \hat{r}}{r^2})$$ which should give us $$3(\vec{m} \cdot \hat{r}) \hat{r} - \vec{m}$$ But I have to derive it using the Einstein summation notation. How can I approach this problem to simplify things ? Should I do something like...
  25. Y

    Deriving commutator of operators in Lorentz algebra

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  26. JD_PM

    Deriving the wave equation using small perturbations

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  27. Arman777

    Deriving the gravitational binding energy of the cluster

    I am trying to derive the gravitational binding energy of the cluster. Its given as $$U = -\alpha \frac{GM^2}{r}$$ Now for the derivation I started from $$dU = -\frac{GM(r)dm}{r}$$ I I tried to write ##dm = \rho(r)4 \pi r^2dr## and do it from there but I could not do much. Any ideas how can...
  28. JD_PM

    Deriving the Equation of Motion out of the Action

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  29. EchoRush

    Deriving the kinetic energy equation?

    Hello, I just have a quick question on deriving the kinetic energy formula using calculus. I understand most of it, I just have a question about one of the steps. here are the steps. Begin with the Work-Energy Theorem.The work that is done on an object is related to the change in its kinetic...
  30. jisbon

    Deriving the expression for average vertical force

    Here's what I have done: Let t1 be the time taken for the ball to reach the ground after the first bounce, and ux be the initial speed in the horizontal direction of ball. Also, let v be the speed after the bounce. For horizontal, $$\dfrac {4}{3}H=U_{x}t_{1} $$ For vertical, $$H=\dfrac...
  31. Arman777

    I Deriving the area of a spherical triangle from the metric

    The metric for 2-sphere is $$ds^2 = dr^2 + R^2sin(r/R)d\theta^2$$ Is there an equation to describe the area of an triangle by using metric. Note: I know the formulation by using the angles but I am asking for an equation by using only the metric.
  32. K

    Deriving an expression for change in internal energy

    Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work...
  33. jisbon

    How are the angles involved in deriving magnetic fields for a current loop?

    So I have managed to derive the magnetic field of a current carrying wire, however, I seem to have some enquiries on deriving the one for the loop. In the formula where ##\frac {ds * r} {r^2}##, I know that it will become ##ds sin \theta.## However compared to the theta in the wire, the theta...
  34. L

    Deriving an equation for theta via the Projectile Motion Trajectory Eq

    Perhaps I should ask this question in the math section of these forums. But, I'm stumped and I don't think this equation is solvable? Find theta given all the other variables:
  35. jisbon

    Deriving expression for magnetic field at point P due to current

    So I think I do understand how to do this, but the thing is my answers are always incorrect. Will need some guidance/help on this. ##B =\frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} ## ##y = Rtan\phi## ##dy = Rsec^2\phi d\phi## ##B = \frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} =...
  36. M

    Kinematics Homework Question- Deriving an expression

    I have been attempting this physics problem for a while now. I am not sure how to begin to attempt this problem with the equations of motion formulas.
  37. C

    Deriving an Expression for an Electric Field along the Z axis

  38. maistral

    A Deriving the derivative boundary conditions from natural formulation

    PS: This is not an assignment, this is more of a brain exercise. I intend to apply a general derivative boundary condition f(x,y). While I know that the boxed formulation is correct, I have no idea how to acquire the same formulation if I come from the general natural boundary condition...
  39. A

    A Deriving an inequality from a paper

    Hi, I am studying a paper by Yann Bugeaud: http://irma.math.unistra.fr/~bugeaud/travaux/ConfMumbaidef.pdf on page 13 there is an inequality (16) as given below- which is obtained from - , on page 12. How the inequality (16) is derived? I couldn't figure it out. However one of my...
  40. A

    Deriving the magnitude range of the force F for which van does not tip over

    Okay so I'm not quite sure about the normal reaction forces. The condition is that they are both equal for the sum of frictional forces to be zero but then technically when substituting into the number equations in place of [ n(1) + n(2) ] either 2n(1) or 2n(2) makes me confused as then n(1)...
  41. D

    I Deriving tensor transformation laws

    Hi, I'm worried I've got a grave misunderstanding. Also, throughout this post, a prime mark (') will indicate the transformed versions of my tensor, coordinates, etc. I'm going to define a tensor. $$T^\mu_\nu \partial_\mu \otimes dx^\nu$$ Now I'd like to investigate how the tensor transforms...
  42. Y

    Deriving Bernoulli's Equation Using Euler's Law of Motion

    Hi all, I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure...
  43. TobilobaEinstein

    B Deriving the Lorentz transformations

    I have tried to derive the lorentz transformations but there is a part of it that requires substitution into two equations when t=0. How do I do that
  44. Aleoa

    Deriving the lever law using infinitesimals

    I'm trying to derive the lever law by myself, however, I'm stuck. Please follow the logic of my calculations. Every object in the picture has the same mass. I want to prove that, under the effect of the gravitational force, I can replace the objects in A and C with the two objects in B, and...
  45. S

    I Deriving E&B Fields from Plane Wave 4-Potential

    I'm trying to derive the electric and magnetic fields of a plane wave from the four-potential ##\mathbf{A} = (A^t , \mathbf{a}) ## in the Lorenz gauge. Given: ##\mathbf{A}(\mathbf{R}) = \Re \left( \mathbf{C} e^{i \mathbf{K} \cdot \mathbf{R}} \right)## for constant future-pointing lightlike...
  46. maistral

    A Deriving the FEA formulation using triangular elements

    Hi, it's been a while since I last posted. Anyway, so I went through the trouble of enrolling in two finite element analyses classes and yet, they still don't teach how the 2D formulation has been made. I'll list the things that 'I know' already to get some things clear. I know how to derive...
  47. TIF141

    Relationship between k and E when deriving the density of states

    Number of states in that volume of k-space, ##n(k)dk## is: $$n(k)dk = (\frac{L^3}{4 \pi^3}) \cdot 4 \pi k^2 dk = \frac{L^3}{\pi^2}dk$$. Then the notes state that by defintion, ##n(k)dk = n(E)dE##, and hence $$n(E)d(E) = \frac{L^3}{\pi^2}dk$$. I don't quite see why this is true - isn't it the...
  48. N

    Deriving Voltage from the Inductor Equation

    Homework Statement L = 20mH = 20 x 10-3 H i = 40 mA for t≤0 i = A1e-10,000t + A2e-40,000t A for t≥0 The voltage at t=0 is 28 V. I have to find the equation for the voltage for t>0. Then I have to find the time when power is zero. Homework Equations v(t) = L* di/dt p(t) = L*i* di/dt The...
  49. ibkev

    I Dot product definition: deriving component form

    ## \newcommand{\ihat}{\hat{\boldsymbol{\imath}}} \newcommand{\jhat}{\hat{\boldsymbol{\jmath}}} \newcommand{\khat}{\hat{\boldsymbol{k}}} ## Several times now I've seen the following technique for deriving the component form of the dot product. It always felt clean and simple until last night when...
  50. Q

    I Deriving the spherical volume element

    I’m trying to derive the infinitesimal volume element in spherical coordinates. Obviously there are several ways to do this. The way I was attempting it was to start with the cartesian volume element, dxdydz, and transform it using $$dxdydz = \left (\frac{\partial x}{\partial r}dr +...
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