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. K

    Deriving Expectations (i.e. mean)

    Deriving Expectations (i.e. means) I'm looking at my Introduction to Econometrics book and trying to figure out the derivations in the 2nd Chapter. First, E(Y^{2}) = \sigma^{2}_{Y}+\mu^{2}_{Y} The derivation goes like this: E(Y^{2}) = E{[(Y - \mu_{Y})+ \mu_{Y}]^{2}} = E[(Y- \mu_{Y})^2] +...
  2. N

    Deriving Jeans' Result from Magnetic Vector Potential

    I'm trying to get from the magnetic vector potential \vec{A}(\vec{x},t) = \frac{1}{\sqrt{\mathcal{V}}}\sum_{\vec{k},\alpha=1,2}(c_{\vec{k}\alpha}(t) \vec{u}_{\vec{k}\alpha}(\vec{x}) + c.c.) where c_{\vec{k}\alpha}(t) = c_{\vec{k}\alpha}(0) e^{-i\omega_{\vec{k}\alpha}t}...
  3. C

    Deriving gravitational redshift using the energy change approach

    An extremely elementary question but... Lets say we had a spaceship sitting on Earth under the influence of gravity. Light travels from the ship's floor to the ceiling. An observer 'A' stands near the ceiling. Hence the light loses gravitational potential energy, and therefore decreases...
  4. P

    For Deriving De Broglie' Wavelength

    Homework Statement The De Broglie Wavelength of any object in motion is given by \lambda=\frac{h}{P} where h is Planck's constant and P is the body's momentum. for heavy masses this wavelength is too small to be observed, nevertheless it is still there... I have seen a derivation for this...
  5. L

    Deriving the head-on collision equation in terms of v2' and v1'

    [SOLVED] Deriving the head-on collision equation in terms of v2' and v1' I think I'm having an algebra issue here, but how is the momentum equation (where v2=0): m1(v1-v1')=m2v2' combined with v1+v1'=v2' to give: v2' = v1 [ 2m1/(m1+m2)] and v1' = v1 [(m1-m2)/(m1+m2)] I'm...
  6. E

    How Do I Integrate e^{iz^2} to Obtain the Fresnel Integrals?

    Homework Statement Integrate e^{iz^2} around the contour C to obtain the Fresnel integrals: \int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4} The contour consists of three parts: z = x, 0 \le x \le R z = Re^{i\theta}, 0 \le \theta \le \pi/4 z =...
  7. A

    Deriving Conservation of Mass & Momentum for an Inviscid Compressible Gas

    Homework Statement Starting from the equations of conservation of mass and momentum for an inviscid compressible gas, \frac{\partial \rho}{\partial t} + \bigtriangledown . (\rho {\bf u}) = 0 \rho ( \frac{\partial {\bf u}}{\partial t} + ({\bf u}. \bigtriangledown){\bf u}) = \bigtriangledown...
  8. P

    Question about Deriving the de Broglie Wavelength

    Something has always bothered me about the way the de Broglie relation is derived and I've never seen anyone address this, so I'm hoping someone here can. As I understand it, the derivation begins with two of Einstein's equations: E=hf, and E=pc. E=hf was experimentally obtained by Einstein...
  9. A

    Deriving angular frequency for simple harmonic motion

    Homework Statement Derive the equation for angular frequency for simple harmonic motion of a spring. Homework Equations Derive omega = sqrt(k/m) from F = -kx (sorry i don't know how to use notation) The Attempt at a Solution I asked my teacher how to do this, and he used some...
  10. G

    Deriving Electric Field from Voltage

    This is probably more Calculus than it is physics. The voltage at a point X produced by a uniformly charged rod is V = (Ke*Q/l)*[ln(l+sqr(l^2+a^2))-ln(a)], in which point X is right above the left end of the rod by a distance a, l is the rod's length, Q is the charge of the rod, and Ke as the...
  11. T

    Deriving the line element in homogenous isotropic space

    If the Ricci-scalar R is constant for a given spatial hypersurface, then the curvature of that region should be homogenous and isotropic, right? A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry): d\sigma^2 =...
  12. J

    Help with deriving Lorentz Factor

    Homework Statement I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage.. 2. Homework Equations / attempt Let: c = velocity of light. v = the velocity as observed from where time t is measured. D = distance AB. t = time light occupies to...
  13. K

    Deriving x(t) into A sin (\omega*t + \varphi)

    Homework Statement Derive... x(t)=(exp^(-\zeta\omegat))*(a1(exp^(i\omegasqrt(1-\zeta^2)*t)))+a2(exp^(-i\omegasqrt(1-\zeta^2)*t)))) into x(t)=(exp^(-\zeta\omegat))*(A sin (\omega*t + \varphi)) Homework Equations n/a The Attempt at a Solution I've managed to get x(t) =...
  14. S

    Deriving Law of Conservation of Energy from E=MC2

    Hello, First post. Thank you for letting me be a part of the discussion. My question is, can the Law of Conservation of Energy, http://upload.wikimedia.org/math/2/7/3/273abc16486177bf6cc4c8ec4a4a5fc9.png, be derived using E=MC2. I understand that the E=MC2 can be derived using the LoCE...
  15. A

    Help Deriving formula for Einstein Radius

    I have been trying to show that the Einstein ring radius R_e = 2[GMx(L-x)/(Lc^2)]^1/2 to no avail. can someone who knows this show me, or at least point out the direction. I have a strong hunch that i'll have to use the light bending formula for small angles  delta_phi = 4GM/(bc^2), and...
  16. F

    Deriving Electric Field Energy Density: A Guide

    Homework Statement I found on Wikipedia the formula for energy density of an electric field in a vacuum to be U = \frac{1}{2}\epsilon_0 E^2. I was wondering if someone could point me in the right direction to figure out how this was derived. Homework Equations The Attempt at...
  17. R

    Help deriving Lagrange's Formula with the levi-civita symbol

    Ok, so I'm really at a loss as to how to do this. I can prove the formula by just using determinants, but I don't really know how to do manipulations with the levi-civita symbol. Here's what I have so far: (\vec{B} \times \vec{C})_{i} = \epsilon_{ijk}(B_{j}C_{k})\vec{e_{i}} And I'm...
  18. T

    Deriving the Doppler Effect

    Homework Statement I have a problem that asks to derive the doppler effect for the two different cases of a moving observer and a moving source. Homework Equations I should get f' = f*(v +/- vo)/(v +/- vs) as my general equation, where f' is the observed frequency and f is the...
  19. G

    Projectile Motion: Deriving an Expression for g

    Projectile Motion! Please Help! Homework Statement The acceleration due to gravity can be measured by firing a projectile upward and measuring the time it takes to pass two given points in both directions. The figure below is a plot of height versus time and shows that the time the...
  20. T

    Deriving the trajectory of the particle

    Homework Statement There is a uniform electric field E, and a uniform magnetic field B in space. A particle of mass m, and charge q, at the origin is released from rest at t=0. The only acting force on the body is the Lorentz force. Derive the trajectory of the particle for t>=0. Homework...
  21. R

    Deriving Gauss's Law Without Coulomb's Law

    Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how? Thanks
  22. D

    Deriving Laplace Transforms

    Homework Statement Derive the Laplace transform of the following functions, using first principles 3d) u(t - T) \} = 0, \ t<T \ (= 1, t>T) 3e) f(t) = e^{-a(t-T)}u(t-T) Homework Equations see above The Attempt at a Solution I know I need to derive the transform using by integration...
  23. M

    Deriving Shear Stress on a Conical Bore Fluid Element

    I would like to derive a relation for shear stress on a conical bore shaped fluid element. Essentially, I have flow going through a converging nozzle. I know variables in this include length of the nozzle, inlet and outlet diameters and pressures and nozzle angle. I've done a force balance on...
  24. C

    Deriving T(\theta,\tau) from Definition of $\otimes$

    Hi, I have a quick question about a derivation that has annoyed me all day. I am trying to prove, from the definition of \otimes that: T(\theta,\tau)=T^{i\alpha}(e_i,f_\alpha) Where \theta \in V^* and \tau \in W^* T: V^* \times W^* \mapsto \mathbb{R} and where V has basis e_i and W has basis...
  25. A

    Deriving the moment of inertia for a sphere

    Homework Statement Derive the moment of inertia for a solid sphere with a uniform mass Homework Equations I= \sum mr^{2} The Attempt at a Solution I decided to change everything to polar coordinates. Since the polar coordinate substitution is \int\int\int_{v} Fr^{2}sin(\phi)drd\phi d\theta...
  26. F

    Deriving Equation Vin = Vout * R2/(R1+R2)

    I have a bit difficulties deriving the equation V in =Vout * R2/(R1+R2) Because I can't see a closed loop here Can someone help with this Thx
  27. R

    Deriving the cooridinate numbers of both ions in rock salt

    How would I go about deriving the cooridinate numbers of both ions in rock salt, and, how could I account for the differences in lattice enthalpy between the following; LiCl (861 kJ/mole) - NaCl (787) LiCl - LiF (1046) LiCl - MgO (3850) Cheers.
  28. M

    Deriving Relations from tanA=y/x

    Given tanA=y/x.....(1) Can anyone tell me how you get the following relations: =>sinA=ay/sqrt(x^2+y^2).....(2) =>cosA=ax/sqrt(x^2+y^2)....(3) where a=(+/-)1 I know tanA=sinA/cosA and sin^2(A)+cos^2(A)=1...and I can see by substituting (2) and (3) into (1) it works, but I really...
  29. U

    Deriving the Value of an Exponent

    Homework Statement Suppose we lived in a matter-dominated, critical-density universe. The matter density rho of such a universe changes with time t as a power of t. Derive the value of the exponent n in the following equation: Homework Equations rho = At^n where A = constant
  30. R

    Deriving the equation for magnetic induction

    Homework Statement We have a straight wire with radius R. What is the magnetic induction through point A at a distance of r? In other words, derive the equation B=\frac{\mu_{0}i}{2\pi r} by using d\vec{B}=\frac{\mu_{0}i}{4\pi r^2}(d\vec{l} \times \vec{u_{r}}) Homework Equations...
  31. 1

    Why Is µ Equal to tan θ in Friction Calculations?

    Homework Statement Deriv µs = tan θ For when a block is put on a wooden plank and the plank is lifted at one side. Homework Equations tan = sin/cos Ff = µFn The Attempt at a Solution Ff = µFn -mgsinθ= µ (-mgcosθ) µ =(-mgsinθ) /(-mgcosθ) µ = tan θ Where i am confused is why Ff...
  32. P

    Deriving 3D Wave Eq.: Assumptions & Considerations

    when we derive the wave equation for a an o0ne dimensional wave moving at constant speed we assume that the wave move losslessly that is a plot of \psi(x,t) with x at any time t is same to the extent that one can be obtained from the other by translation. similarly what are the assumptions when...
  33. C

    Deriving Ji's Sum Rule - Help with Steps from Diehl Paper

    Dear all, I am new here and hope that I write this in the right place. ;-) I am seeking help in deriving Ji's Sum Rule, which tells you that the second moment of the nucleon's GPDs equals the total angular momentum of the quarks. E.g. in Diehl, hep-ph/0307382, Sect. 3.6. The step where...
  34. F

    Deriving Formulas for Vmin & Vmax on Glare Ice w/ Zero Friction

    Homework Statement A circular curve of radius R in a new highway is designed so that a car traveling at speed v can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will...
  35. Hans de Vries

    Deriving the Dirac propagator 'purely' from causality

    I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...
  36. ~christina~

    Deriving the velocity from a distance equation

    Homework Statement x(t)= (7.00m/s)t + (7.00m/s^2)t^2 - (2.00m/s^3)t^3 a) find the expression for the velocity as a function of time. b) plot the graphs of the position, velocity and acceleration as accleration vs time for the interval given. c) At what time(s) btw t=0 and t= 3.00...
  37. W

    Deriving an Infinite Series: P_e = 5/3

    Homework Statement I am wondering if someone could give me some insight on how the following infinite series was derived: P_e = \sum_{-\infty}^\infty (1/2)^{2|n|} = -1 + 2 \sum_{n=0}^\infty (1/2)^{2n} = 5/3 Homework Equations See above The Attempt at a Solution I think the -1...
  38. ~christina~

    Deriving the rate time equation for a Jerk (J)

    Homework Statement Automotive engineers refer to the time rate change of acceleration as the Jerk. Assuem an object moves in 1 dimention such that it's Jerk is constant. a) determine expressions for it's 1. acceleration ax(t) 2. velocity vx(t) 3. position x(t) given initial...
  39. A

    Deriving classical potentials from tree diagrams

    I'm looking for a good book for graduate students that indicates how one can obtain a (classical) potential from a tree-level Feynman process. For example, how can one go from the S-matrix of e.g. Compton scattering and derive the Coulomb potential. Any help would be appreciated.
  40. C

    Deriving Taylor Series: Understanding the Step Escaping Me

    I was going through the derivation of the Taylors series in my book (Engineering Mathematics by Jaggi & Mathur), and there was one step that escaped me. They proved that the derivative of f(x+h) is the same wrt h and wrt (x+h). If someone could explain that, Id be really grateful.
  41. A

    Physics Lab - Projectile Motion - Deriving a Position Vector

    Homework Statement Okay, this lab has had me stumped for the last few hours. This is our first lab for AP Physics BC. Problem: Determine the position vector that describes the locatino of the water that is launched by a drinking fountain. Your position vector needs to be in unit vector...
  42. R

    Derive Equation for Launch Angle | Physics Solved Variables

    How do you derive the equation for the launch angle using the range and peak equations? This isn't a homework problem but something i want to know for my own general knowledge for solving physics problems. Is there a site that has physics equations solved for different variables? Hyperphysics is...
  43. L

    Deriving a kinematic equation.

    Homework Statement Derive (v_f)^2 = (v_i)^2 +2ad Homework Equations (v_f)^2 = (v_i)^2 + 2ad (v_f) = (v_i) + at d = (v_i)t + \frac{1}{2}at^2 The Attempt at a Solution I have attempted to replace the variables with others from other kinematic equations such as v_f = v_i + at...
  44. R

    Deriving the Surface Area of Sphere

    How do we come to 4.pi.r^2?
  45. J

    Deriving input-output relationship

    hi frenz i want to how to derive mathematical relation between dependent(output) and independent(input) variables when i know the relation between them at few samples. cud someone help me out? thanks in advance
  46. X

    Deriving equations on Einstein's 4th paper

    Homework Statement I need to derive some equation that are on the paper "does the inertia of a body depend on it's energy content". http://www.fourmilab.ch/etexts/einstein/E_mc2/www/" I just don't know where to start and if someone can point me to the right direction, it will be so much...
  47. H

    Deriving a trigonometric identity

    For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...
  48. C

    Deriving equation for electrostatic force.

    Homework Statement Basically I am given an image showing a test charge tied to a string where there is the ball is stationary. I need to use the fact that there is no net force on the ball to derive an equation for the electrostatic force in terms of g, the angle, and the mass of the ball...
  49. D

    Deriving an Equation to Find Width of Hallway from Two Ladders

    Two ladders, one red, and the other green, are 2 and 3m long respectively. The base of the red ladder is resting on the side of a narrow hallway and leaning on the wall of the other side of the hallway. The green ladder is doing the same, but on the opposite side, such that the two ladders cross...
  50. C

    Deriving Velocity Profiles for Flow of Oil Down Glass Rod

    I am having a huge problem with understanding the derivation of velocity profiles for these type of problems. The one i am having the most difficulty is the flow of oil going down vertically along the surface of a glass rod. Where p=900 kg/m^3 and u=120 mPa's. How do I start this problem?
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