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. Y

    Question on a step in deriving Poynting Theorem.

    This is in page 346 of Griffiths "Introduction to Electrodynamics". This is regarding to work done by electromagnetic forces dW acting on charges in the interval dt . dW = \vec F \cdot d \vec l =q( \vec E + \vec v X \vec B) \cdot d \vec l = q( \vec E + \vec v X \vec B) \cdot \vec v d t...
  2. Y

    Deriving equation of stored electrical energy in a charge distribution.

    I have problem understanding why the surface integral disappear when taking the volume to very large in this equation: W_e = \frac 1 2 \int_{v'} \rho_v V dv' = \frac 1 2 \int_{v'} (\nabla \cdot \vec D)V dv' = \frac 1 2 \int_{s'} V \vec D \cdot \hat n ds' \;+\; \frac 1 2 \int_{v'} \vec E...
  3. O

    Deriving Speed In Terms of Potential Difference

    I'm attempting to derive speed in terms of potential difference (voltage), can anyone let me know if there are any errors? http://www.texify.com/img/%5CLARGE%5C%21E_k%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7Bmv%7D%5E2.gif...
  4. J

    Deriving EOM of cantilever beam using specific Lagrangian

    Homework Statement The specific Lagrangian for a cantilever beam is given by: \overline{L}=\frac{1}{2}m[\dot{u}^2(s,t)+\dot{v}^2(s,t)]-\frac{1}{2}EI[\psi ^{\prime}(s,t)]^2 where m,EI are mass and bending stifness, respectively. \dot{u},\dot{v} are velocities in u,v directions...
  5. G

    Deriving an acceleration from Potential Energy

    Homework Statement A 4 kg particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U(x) = ax^2 + b, where a = 6J/m^2 and b = 2J. What is the x-component of the acceleration of the particle when it is at x = 1 mHomework Equations deltaU = -W...
  6. J

    Deriving the rate of change of the radius of a moving particle in a cyclotron.

    The question: A particle in a cyclotron gaines energy q \Delta V from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T = \frac{2 \pi}{\omega} = \frac{2 \pi m}{q B} so the particle's average rate of increase in...
  7. O

    Deriving Focal Length for a Thick Lens

    Homework Statement Derive 1/f = (n-1)*( (1/r1)-(1/r2)+(((n-1)t))/(nr1r2))) using the ray matrix method. Homework Equations Matrix for curved dielectric interface: M1 = [1, 0] [(1/r)(n1/n2 - 1), n1/n2 ] Matrix for translation through homogeneous medium: M2 = [1, d] [0...
  8. S

    Deriving Electromagnetic Theory

    Hi, I am trying to re-derive, or should I say modify, the existing theory of classical electromagnetism by postulating the existence of magnetic monopoles. Where should I begin?
  9. 7

    Where did I go wrong in deriving potential energy?

    Hello, i am trying to derive flexible energy, but i get a negative sign in front of a Work (A). Where did i miss? F is force of a spring. I don't know if i used Hooke's law correctly... Thank you for looking.
  10. R

    What is the Mistake in Deriving the EM Hamiltonian?

    For some reason I can't derive the Hamiltonian from the Lagrangian for the E&M field. Here's what I have (using +--- metric): \begin{equation*} \begin{split} \mathcal L=\frac{-1}{4}F_{ \mu \nu}F^{ \mu \nu} \\ \Pi^\mu=\frac{\delta \mathcal L}{\delta \dot{A_\mu}}=-F^{0 \mu} \\...
  11. jegues

    Deriving Corner Frequency for High Pass Filter

    Homework Statement See Explanation below for details of my confusion. Homework Equations The Attempt at a Solution Hello all, I've derived a transfer function, T(s) = \frac{\frac{-R_{2}}{R_{1}}}{1 + \frac{1}{sCR_{1}}}, but I can't seem to derive the corner frequency...
  12. A

    Deriving Total Energy of a Binary System

    Homework Statement Beginning with the kinetic and potential energies of two objects with masses m1 and m2, show that the total energy of a binary system is given by: E=\frac{1}{2}\muv2 - G\frac{M\mu}{r} Homework Equations The one given K =\frac{1}{2}mv2 U = G\frac{Mm}{r} The...
  13. King Tony

    Deriving the transport equation (PDE)

    Homework Statement Attached image please, sorry I tried LaTeXing and i failed super hard. Homework Equations Fundamental Theorem of Calculus Multivariate chain ruleThe Attempt at a Solution I'm basically at a loss of words on this question. I might be thinking of this incorrectly but what my...
  14. M

    Deriving properties of the Gamma Function

    I was just curious as to how I can show the following properties of the Gamma Function, they came up in some lecture notes but were just stated? Notation: G(z) = Gamma function 2^(z) = 2 to the power of z I = Integral from 0 to infinity (1) G(z)*G(1-z) =...
  15. D

    Problem in deriving Ampere's law

    Homework Statement I'm going through Jackson a bit, reading on Magnetostatics, and I came into a bump. I'm looking at \nabla\times B=\frac{1}{c}\nabla\times\nabla\times\int\frac{j(r')}{|r-r'|}d^3r' I expand that using 'BAC-CAB' rule and I get: \nabla\times...
  16. Saladsamurai

    How to Derive 2D Navier-Stokes Equations for Steady Flow Using a Control Volume?

    Homework Statement I need to derive the 2D N-S equations for steady, incompressible, constant viscosity flow in the xy-plane. I need to use a control volume approach (as opposed to system approach) on a differential control volume (CV) using the conseervation of linear momentum...
  17. G

    Deriving a formula for max. speed of a simple pendulum bob

    Homework Statement Derive a formula for the maximum speed V_max of a simple pendulum bob in terms of g, the length l and the maximum angle of swing Θ_max. (Hint: Use the fact that the same amount of energy at the top of the arc is the same as at the bottom of the arc.) The picture depicts...
  18. P

    Deriving forces from an energy potential

    Homework Statement This is not a homework problem. I'm trying to do this for research purposes. I have an energy potential (the Keating potential) of the following form (attached). In this form, A, B, and C are force constants, and r_ab is the vector along the bond between atoms a and b...
  19. L

    Deriving the Nambu-Goto Equation of Motion

    http://www.damtp.cam.ac.uk/user/tong/string/string.pdf In these notes, I am trying to derive the equation of motion (1.21) corresponding to the Nambu-Goto action: \partial_\alpha ( \sqrt{ - \text{det} \gamma} \gamma^{\alpha \beta} \partial_\beta X^\mu ) =0 I have found and proved all...
  20. M

    Deriving f(x)=(x^2+5x+2)^4 & Finding Tangent with y=160x+16

    f(x)=(x^(2)+5x+2)^(4) f'(x)= 4(x^2 + 5x + 2)^3 (2x + 5) = 8x + 20(x^2 + 5x + 2)^3 is this right than my equation of the tangent turned out to be y=160x +16
  21. A

    Deriving the lens formula for a convex lens-say

    I will be thankful if the following points are clarified. 1. While deriving the lens formula for a convex lens-say, 1/f= 1/v - 1/u where u and v are the object and image distances, the minus sign is obtained after applying sign conventions. But, I don't understand the logic behind taking the...
  22. E

    Deriving Linear Transformations - Special Relativity

    I wasn't sure if this counted as intro physics. Feel free to move if I have it in the wrong place. Homework Statement In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light. Describing the reference frames: s' -> x'=u't'...
  23. T

    Deriving the mass conservation integral in GR

    Homework Statement Starting from a general axisymmetric metric ds^2=g_tt dt^2 + 2g_tφ dtdφ +g_φφ dφ^2 + g_rr dr^2+g_θθ dθ^2 ...(0) where the metric components are functions of the coordinates r and θ only. I've managed to show (via Euler-Lagrange equations) that g_tt dt/dτ + g_tφ...
  24. A

    Deriving length contraction using Lorentz invariants

    Homework Statement Derive length contraction using Lorentz invariants. Homework Equations ds^2 = dx^2 +dy^2 + dz^2 - c^2 dt^2 The Attempt at a Solution Consider a rod parallel to the x-axis and moving with velocity v in the x-direction. We can measure the length of the rod of...
  25. T

    Deriving Mid-Span Deflection of Simply-Supported Beam

    someone please help not sure were to start. use the method of area-moments to derive an expression for the mid-span deflection of a simply-supported beam with the following properties: Span= L : second moment of area of section= I : modulus of elasticitiy= E which has a total UDL along...
  26. G

    Deriving transformation matrix from clues

    I have PTV=R where P and T are square matrices (4x4) and V and R are non-square (4x3). P and V are known, T is unknown, and R is partially known (3 unknown elements). Seems impossible, but T is a transformation matrix (ie upperleft 3x3 is a rotation matrix) which gives me additional clues...
  27. P

    Deriving Relation between Angular & Translational Velocities in Circular Motion

    relationship of angular velocy and translational velocity in simple circular motion?? Like if something is going in a circle of radiues R at speed v with angular velocity w, then w=v/R. Where does this relation come from? I'm having trouble deriving it. Please help! EDIT: I think i got it...
  28. N

    Underdamped motion (Formula deriving)

    Homework Statement I'm trying to derive the equation of motion of underdamped motion. Homework Equations From F = m\ddot{x} -kx - c\dot{x} = m\ddot{x} m\ddot{x} + c\dot{x} + kx = 0 x_{h}(t) = ae^{\lambda t} \dot{x}(t) = \lambda ae^{\lambda t} \ddot{x}(t) = \lambda^2 ae^{\lambda t}...
  29. L

    Problems deriving tensor equations

    On page 14 in the notes attached in this thread: https://www.physicsforums.com/showthread.php?t=457609 (i)In the definition given just above eqn 22, it says "In other words, \phi_\alpha \cdot \lambda is a smooth map from I to \mathbb{R}^n for all charts \phi_\alpha. Where do they pull this...
  30. C

    Help Needed: Deriving Expressions for Mass-Spring System

    Could somebody help me in deriving the following expressions? I can judge that the first equation is a common expression for finding Keq for a mass-spring system in series.. Can't do the rest :/ anybody please ? Thanks in advance.
  31. soothsayer

    Deriving Relativistic Momentum

    I'm having some problems trying to figure out how to derive relativistic momentum. The way it was explained to me, classically, p=mv=m(dx/dt),but dx/dt is measured differently in different reference frames. So, if you look at time dilation, t=ɣt' where ɣ= 1/(1-(v/c)^2)^1/2 and t' is time in the...
  32. D

    Deriving the Schwarzschild solution

    Right so there's this part in my notes where we begin to derive the schwarzchild solution. There's a substitution part I don't understand fully (I think) but I'll start from the beginning...The Schwarzschild Solution. The solution corresponds to the metric corresponding to a static, spherically...
  33. G

    Deriving the Lorentz Boost for an Arbitrary Direction

    Homework Statement So, I'm working through a relativity book and I'm having trouble deriving the Lorentz transformation for an arbitrary direction v=(v_{x},v_{y},v_{z}): \[\begin{pmatrix} {ct}'\\ {x}'\\ {y}'\\ {z}' \end{pmatrix}=\begin{pmatrix} \gamma & -\gamma \beta _{x} &...
  34. R

    Deriving Variation of Parameters for Systems

    1.Homework Statement We know the derivation of the method of variation of parameters for second order scalar differential. The task is to derive the method of variation of parameters for scalar equations using this approach: first convert the scalar equation into the first order system and...
  35. J

    Deriving mass of Earth from definition of gravity

    Homework Statement Using the definition of gravity, derive the mass of the Earth Homework Equations I am unsure if this is simply a plug n chug problem and I am over thinking it or there is some way to use calculus to derive the mass from the gravity equation. The Attempt at a...
  36. G

    Deriving Equation for Water Depth After Tank Hole Poked

    Homework Statement A vertical cylindrical tank of cross-sectional area A_1 is open to the air at the top and contains water to a depth h_0. A worker accidentally pokes a hole of area A_2 in the bottom of the tank. Derive an equation for the depth of the water as a function of time t after...
  37. H

    Buoyancy problem: Deriving an equation for volume of a floating object

    Homework Statement The problem consists of a ball almost completely submerged. The exact question is: "An object with density ρO and mass m is floating in a pool of fluid with density ρF. Derive an expression for the volume of the object that is above the fluid." Homework Equations...
  38. R

    Help with deriving an equation (coloumb's law, pith ball charges)

    Homework Statement A lab we were recently given in AP Physics class contained an equation already derived. This lab was about determining the charge on a pith ball, using the static charge of a fur to charge the balls negatively, so they repel. Finding the angle and distance between the two...
  39. J

    Problem deriving Einstein tensor form Bianchi identity

    1. I can't understand one step in the derivation of the Einstein tensor from the Bianchi identity.I have looked in a lot of books and all over the internet and everyone glosses over the same point as if its obvious, but it isn't obvious to me. 2. Below is the entire derivation. It seems...
  40. V

    Deriving pressure, density and temperature profile of atmosphere

    Homework Statement Derive the pressure, density and temperature profiles of an adiabatically stratified plane-parallel atmosphere under constant gravitational acceleration g. Assume that the atmosphere consists of an ideal gas of mean molecular weight \mu. Given \mu=14u, g = 9.81m/s^2, z =...
  41. B

    Deriving the equations of motion in f(T) gravity

    Hi there, I originally posted this in the SR, GR section so sorry for the re-post. Can anyone point me in the direction of any papers that explicitly derive the equations of motion in f(T) gravity. I have seen the wikipedia derivation in f(R) gravity but can't find anything for f(T) where...
  42. A

    Deriving the formula for a partially filled sphere using spherical polars.

    Homework Statement Deriving the formula for a partially filled sphere using spherical polars. Note this is not a homework problem , I have solved it using a cylindrical slice method, just been bugging me about how to obtain the same result using spherical polars.if the sphere has a radius a...
  43. L

    Deriving the Lie Derivative of a Covector: The Leibniz Rule

    Use the Leibniz rule to derive the formula for the Lie derivative of a covector \omega valid in any coordinate basis: (L_X \omega)_\mu = X^\nu \partial_\nu \omega_\mu + \omega_\nu \partial_\mu X^\nu (Hint: consider (L_X \omega)(Y) for a vector fi eld Y). Well I have the formula L_X(Y) =...
  44. Z

    Deriving the Distance Between Orthocentre & Circumcentre of a Triangle

    The problem Can anyone explain me a step given in my book? This is actually the derivation of the distance between orthocentre and circumcentre of a triangle using vectors. ABC is a triangle. S is the circumcentre and H is the orthocentre. \vec{SA} + \vec{SB} + \vec{SC} = \vec{SA} +...
  45. S

    Deriving the dielectric constant of water

    We derived a formula to calculate the dielectric constant for some materials. It works well for gases and some liquids. But, water has a extraordinary dielectric constant of ~80. I tried googling it up but couldn't find any place which explains (mathematically) why it's so big. The professor...
  46. R

    Deriving Coulomb's Law from Gauss' Law

    Homework Statement When I try working out the example below from PlanetPhysics, I wind up with 2PI rather than 4PI in my answer. Should I be considering my result valid for only a hemisphere and double it for a sphere--or am I just making a mistake in my math? "As an example of the...
  47. T

    Deriving Equations for Particle Motion and Momentum Conservation

    Homework Statement [PLAIN]http://img51.imageshack.us/img51/4562/mecj.jpg Homework Equations The Attempt at a Solution How do I go about showing LHS = RHS in each of these? (\wedge denotes cross product) What is \dot{r}=\dot{x_1}-\dot{x_2} and \dot{R} ?
  48. K

    Deriving Equation (3) from A. Zee's "QFT in a Nutshell" Chapter I.5

    In A. Zee "QFT in a nutshell" in chapter I.5 on page 31 how does equation (3) come about? Just the line above this equation, he gives an equation which needs to be rearranged to give (3). It must be embarrassing simply, but I can't see how. Something with the indices goes on. How does the...
  49. S

    Deriving equations from fourier series representations

    Say you have the coefficients a_k of a Fourier series representation of some function x(t). You can easily then give x(t) as $$x(t) = \sum_{k = -\infty}^{\infty} a_k e^{i k \omega_0 t}$$ But this doesn't do much good in telling you what the actual function looks like. For example, if we have...
  50. M

    Deriving Maxwell's Relation with Thermodynamic Variables

    Homework Statement Derive the following general relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \frac{1}{C_{V}} T \left(\frac{\partial p}{\partial T}\right)_{V} Homework Equations Maxwell's Relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \left(\frac{\partial...
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