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".

View More On Wikipedia.org
Recent contents Top users
  1. C

    Deriving Rotational Energy Equation for Rigid Bodies

    Hello, I think I've got the right idea on how to perform this question but I just need a little bit of help. Homework Statement Show that for a rigid body rotating with angular velocity \omega the energy of rotation may be written as: E = \dfrac {1}{2}I\omega^{2} where the moment of...
  2. S

    Deriving an equation for displacement and acceleration (given velocity)

    Homework Statement For 0<t<1, v(t) = t +3 For 1<t<2, v(t) = 5-t Assume x(o)=0 A) Draw corresponding displacement and acceleration diagrams. B) Determine the equation for each segment Homework Equations Acceleration is the derivative of velocity. Velocity is the derivative of...
  3. R

    Deriving Regression Coefficients

    Hi Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas. I can derive to here: \sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left(...
  4. B

    Deriving Equation #3: (b/2)θ=L(2θ)

    Homework Statement Using equations #1 and #2 to derive equation #3 Homework Equations #1- ∆x = (b/2)theta #2- ∆z= L (2theta) #3- ∆x= ∆z b/4L The Attempt at a Solution Now I set equations #1 and #2 equal to each other, but I'm not sure how the thetas end up cancelling or if I'm even...
  5. C

    Deriving Final Equation from Equations 1 & 2

    HI I need help with the steps in between? I am totally confused... So, how to derive the final equation from equation 1 and 2 m1v1i+m2v2i=m1v1+m2v2f (Equation 1) 1/2m1V1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 (Equation 2) v1i-v2i= -(V1f-v2f) ( Final Equation)
  6. A

    Deriving absolute error equation

    Homework Statement I need to derive an error equation from the following equation... \frac{e}{m} = \frac{2V}{B^{2}R^{2}}Homework Equations Just... basic... derivation rules...The Attempt at a Solution I did try, just don't know how to put the stupid attempt in LaTeX... I'm stuck at the "2V"...
  7. R

    Deriving Planck's Law: Solving for the Integral Formula

    Homework Statement I need to find the Planck's law: R(\lambda)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1} Homework Equations The Attempt at a Solution I've done most of the derivation, but I got stuck with an integral: R(\lambda)=\frac{1}{4\pi^3 \hbar^3 c^2}...
  8. L

    How to Derive Using the Chain Rule for 2x^2+5xy-y^2=1?

    Homework Statement 2x^2+5xy-y^2=1 Homework Equations d/dx(f(u)x))=df/du * du/dx The Attempt at a Solution i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?
  9. TheFerruccio

    Deriving EM Wave Equations from Faraday's & Ampere-Maxwell's Laws

    I am trying to derive the electromagnetic wave equations from Faraday's law of Induction, and the Ampere-Maxwell law. But, I am having a problem with the 1/c^2 disappearing. This is what I am using: \nabla\times\vec{B}=\mu\vec{J}+\mu\epsilon\stackrel{\partial\vec{E}}{\partial t}...
  10. C

    Questions deriving from the Principle of Equivalence

    Hi all, There are a few doubts I hope I can get enlightened. If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab? What I'm confused about also is, why is that when you have an...
  11. P

    Deriving equation to describe lattice vibrations of a one dimensional crystal

    When setting up this derivation one assumes a chain of identical atoms. The interatomic interaction between atoms is short ranged and so only affects neighbouring atoms (see Hook and Hall, "Solid State Physics" chapter 2.3.1). The potential V(r) is expanded as a taylor series about r = a to...
  12. P

    Deriving the Poincare algebra in scalar field theory

    Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...
  13. D

    Explicitly Deriving the Delta Function

    When working with Fourier transforms in Quantum mechanics you get the result that \int_{-\infty}^{\infty}e^{-ikx}e^{ik'x} = \delta(k-k') I understand conceptually why this must be true, since you are taking the Fourier transform of a plane wave with a single frequency element. I have also...
  14. I

    Deriving Bit Error Rates for different diveristy tecniques

    Homework Statement Using the normal distribution for different modulation techniques over rayleigh fading , we have to derive SNR values for different Diversity techniques such as selection combining, Equal Gain Combining and Maximal Ratio Combining. Now for Non-coherent BPSK I have to...
  15. V

    Help deriving expression for the error in velocity.

    Homework Statement Derive the error expression \delta v_{}x from the equation v _{x}=\frac{s}{sqrt(\frac{2h}{g})} The Attempt at a Solution I've derived error expressions before, but I have a history of getting the calculations right and the error equations wrong. So, if possible I'd...
  16. M

    Deriving velocty with drag equation

    Homework Statement Derive an equation for velocity based on time with drag. Homework Equations The equation is: v(t) = F/b (1 - e^(-bt/m)) The Attempt at a Solution There's some math on paper, but I got down to: F - bv = ma a = dv / dt F - bv = m*dv/dt dt = m*dv / (F -...
  17. J

    Deriving parametric equations of a point for the involute of a circle

    Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...
  18. V

    Deriving Equation: g = aave(M + m / m)

    I am supposed to derive this equation: g=aave(M + m / m) It gives me two pairs of equations: T1-Fr = Ma1 mg-T1= ma1 and T2 + Fr = Ma2 mg - T2 = ma2It also says, "hint: for the first pair of equations, eliminate the unknown tension. Do the same for the second pair of equations. In this new...
  19. V

    Deriving Resonant Frequency of Multiple Mass Mass-Spring Systems

    How does one begin to derive the resonant frequencies of a multiple mass mass-spring system? (3-mass system) OK, so deriving this isn't a homework problem. I'd just like to know how. It's been a couple of years since I've taken a physics course. I was asked what the resonant frequencies of each...
  20. snoopies622

    Deriving Special Relativity: Force, Acceleration, and Velocity

    Wikipedia's 'special relativity' entry gives the following relationship between force, acceleration and velocity: \vec f=\gamma m \vec a + \gamma^3 m \frac {\vec v \cdot \vec a}{c^2}\vec v but without derivation. Could someone tell me how one arrives at this? Thanks.
  21. Battlemage!

    Deriving a formula for Impedance for an AC circuit

    Homework Statement Find the impedance of the circuit (R and L in series, and then C in parallel with them). A circuit is said to be in resonance if Z is real; find ω in terms of R, L, and C at resonance. Here is the circuit: http://img382.imageshack.us/my.php?image=g...ccircuitgf5.png...
  22. S

    Deriving equation for circle using sin and cos identities

    Homework Statement I have been given these two equations: x=2acos^2(x) , y = 2a(cos(x))(sin(x)) where a ranges from 0 to 5 and -2π < x < 2π I need to prove that these equations (when you plug in values for x) create points that when plotted, give you a circle with center (x-a) and radius a...
  23. C

    Deriving Velocity Field of Rotating Plate Using v = ω × r

    Homework Statement A thin, circular plate assumed to lie on the xy-plane is rotating about its center, located at (0, 0), with angular speed ω. (ω > 0 means that the plate is rotating in the counterclockwise direction.) Show that the velocity field of of this plate is given by v(x, y) =...
  24. Somefantastik

    How Do You Derive the Fourier Series for Laplace's Equation Solutions?

    I'm supposed to derive this monster! \frac{1}{2} + \frac{2}{\pi} \sum^{\infty}_{k = 1}\frac{1}{2k-1}sin(2k-1)x = \left\{^{0 \ for \ -\pi < x < 0}_{1 \ for \ 0<x<\pi} I don't even know where to start right now. And no examples to work from. Can anyone get me started? the Chapter is on...
  25. Q

    Deriving Identity: A Proof for S^{p}_{n} = 1^p + ... + n^p

    deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^p + ... + n^p the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)^(p+1) - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6 S^{3}_{n} =...
  26. Q

    Deriving Identity: Proving the Sum of Powers Identity with Step-by-Step Guide

    deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^{p} + ... + n^{p} the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)*^{p+1} - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6...
  27. J

    Deriving a thermodynamics relationship

    Homework Statement Derive: \left(\frac{\partial C_{P}}{\partial P}\right)_{T} = -T \left(\frac{\partial^2 V}{\partial T^2}\right)_{P} Homework Equations I have already derived that C_{P} = C_{V} + \left[\left(\frac{\partial E}{\partial V}\right)_{T} + P \right] \left(...
  28. J

    Deriving The Quad. Eq. Using least squares.

    Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.
  29. C

    Deriving Trig Formulas: Solving Problem with Sin and Cos Identities

    hello. i need help deriving trig formulas. the first problem i most derive is 51. sin^2 x + cos^2 x = 1 i can use these identities: a. sin(-x) = -sinx b. cos(-x) = cos(x) c. cos(x+y) = cosxcosy - sinxsiny d. sin(x+y) = sinxcosy + cosxsiny thanks for any help
  30. N

    Deriving the formula for double slit diffraction as in Young from Fraunhofer

    Homework Statement I apologize for the blurriness in my title, I couldn't find anything better to fit within the length limit. The problem I'm stuck with, paraphrased, is to derive the formula for the diffraction pattern of a double slit, as found in the Young experiment, from the Fraunhofer...
  31. H

    Deriving the formula for arctanh(x)

    Homework Statement "starting from the definition of tanhx in terms of exponentials, prove that... arctanh(x)=1/2log((1+x)/(1-x)) This is such a simple equation but I'm having a hard time proving it, can anyone help? Cheers Homework Equations The Attempt at a Solution
  32. B

    Ehrenfest Theorem: deriving d<p>/dt = <-dV/dx>

    I am having trouble with this derivation. This is where I am at: \frac{d \left< p \right>}{dt} = \int \left[ \left( -\frac{\hbar^{2}}{2m}\frac{\partial^{2} \Psi^{*}}{\partial x^{2}} + V\Psi^{*} \right) \frac{\partial \Psi}{\partial x} + \frac{\partial \Psi^{*}}{\partial x}\left(...
  33. B

    Confusion: deriving momentum expectation value in QM

    On pages 16-17 of Griffith's Intro to QM, he writes the following: \frac{d\left\langle x \right\rangle}{dt}= \int x \frac{\partial}{\partial t}|\Psi|^{2} dx = \frac{i\hbar}{2m}\int x \frac{\partial}{\partial x} \left( \Psi^{*}\frac{\partial\Psi}{\partial x}- \frac{\partial\Psi^{*}}{\partial...
  34. H

    Help Deriving formula for moment of inertia lab

    this lab is very similar to mine basically i can only seem to derive a portion of the formula, I=mgb/al - mb^2 where b- radius, g-gravity, al- angular acceleration. I do not get the right answer: here is what i did do however, Fnet=ma T-mg=-ma (acceleration is downwards) so T=(mg-ma) so then...
  35. V

    Deriving Gauss' Law for Gravity from Newton's Law

    Homework Statement How would I derive Gauss' law for gravity from Newton's law?Homework Equations \mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}} to \nabla\cdot\mathbf{g} = -4\pi G \rhoThe Attempt at a Solution I have no reference material outside the wide...
  36. T

    Deriving the continuity equation from the Dirac equation (Relativistic Quantum)

    So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...
  37. J

    Deriving Magnetic Field Through Solenoid Using Amperes Law

    [SOLVED] Amperes Law Homework Statement Deriving the magnetic field through a solenoid. Homework Equations dB = mu0/4pi x Idlsintheta/ r^2 where I = current dl= a tiny change in length dB = a tiny change in flux density sintheta is the angle to the normal r is the radius mu0 is the...
  38. N

    Deriving the Work-Energy Theorem: A Calculus Refresher

    It's been a while since I've taken calculus. I was going through the derivation of the work-energy theorem and came across this: dv/dt = (dv/dx)(dx/dt) which is supposed to be a result of the chain rule. Anyone care to explain and please simplify it as much as possible. Thanks!
  39. B

    Deriving the phase velocity of a wavefunction

    Homework Statement If \Psi = f(x, y) and x = g(t), y = h(t), then (d\Psi / dt) = (p\Psi / px)(dx / dt) + (p\Psi / py)(dy / dt), where "p" symbolizes the partial derivative here and throughout the rest of this posting. Derive the phase velocity equation +/- v = -(p\Psi / pt) / (p\Psi / px)...
  40. P

    Deriving Equations of a Parabola

    Hey, Homework Statement How do you derive the equations of the parabola from the general equation of a Conic Section? Homework Equations General Equation of a Conic Section, {{{A}{{x}^{2}}}+{{B}{x}{y}}+{{C}{{y}^{2}}}+{{D}{x}}+{{E}{y}}+{F}} = {0} Where (for a parabola)...
  41. marcus

    Ashtekar: deriving the covariant entropy bound from LQC

    Here are some papers on the covariant entropy bound conjectured by Raphael Bousso http://arxiv.org/abs/hep-th/9905177 http://arxiv.org/abs/hep-th/9908070 http://arxiv.org/abs/hep-th/0305149 It would be a significant development if the conjectured bound could be proven to hold in LQC...
  42. K

    Deriving the canonical equations of Hamilton

    As i know there are several diffrent way to derive the canonical equations. Some of them starts from a physical principle like Hamilton's principle or the Lagrange equations. But it can be derived also by simply make a Legendre transormation on the Lagrange function and then make...
  43. S

    Help deriving this elliptical orbit equation?

    help deriving this elliptical orbit equation?? Hi guys, this is my first post on these boards. just found out about this forum and I am really happy because i often find i need a place like this to ask questions and my prayers are answered! im a physics/computer science major in my second year...
  44. H

    Deriving Vector and position vectors from Force vector

    Homework Statement An object of mass m is at rest at equilibirum at the origin. At t=0, a new force \vec{F}(t) is applied that has components F_{x}(t) = k1+k2y F_{y}(t)=k3t where k1, k2, and k3 are constants. Calculate the position r(t) and velocity v(t) vectors as functions of time. Homework...
  45. A

    Thermo: Deriving dh=Cp(dT) & du=Cv(dT)

    Why does du/dT = Cv, and same for Cp? Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from: Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M...
  46. M

    Deriving Power Expression for Transverse Traveling Wave

    So in my book, it derives the expression for power in a traveling transverse mechanical wave. P= Sqrt[(mu)F].(omega)^2.(A)^2 It reduces this from: P=k^2.omega^2.F.A^2.(sin(kx-omega.t)^2 Where all symbols are the standard ones in dealing with waves. Could someone please go thru how it...
  47. E

    Deriving a Uniform Circular Motion Equation

    Derive the following equation: (mV^2/r)cos(x) = mgsin(x) I don't know how you would exactly derive the equation but you can simplify it to: tan(x)mg = mV^2 /r You can also divide by the m and get tan(x)g = V^2/r ... Any help is appreciated.
  48. N

    Deriving current expression from the info given

    Homework Statement I am doing some research and reading this: http://www.csuohio.edu/ece/theses/2004/Bhavin.pdf I don't understand how the equation 4.1.11 on page 67 is derived. Can anyone help clarify? Homework Equations (As in the pdf file) The Attempt at a Solution I have...
  49. T

    Deriving Poynting Vector from EM Waves

    can anyone help me derive the poynting vector from energy density of electromagnetic waves? and how we obtain average value <S> thanks
  50. V

    Understanding Newton's Second Law: Deriving the Equation F=ma

    I knew i should have paid more attention in class =/ anyways, We have been studying Newton's second law. And I have a question on my lab that asks for me to "derive equation for a (acceleration) vs F (force) and a (acceleration) vs m (mass)" a vs F and a vs M are two graphs which we did...
Back
Top