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. FeDeX_LaTeX

    Exploring the Speed of Light: Deriving its Formula

    Hello; How is this formula derived? And why is the speed of light squared? Is there a reason for that? Thanks.
  2. Q

    Deriving a vector identity using Pauli spin matrices

    Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...
  3. K

    Deriving Equation: S=W-W2/W-W1=M/M1-M2

    Homework Statement Derive equation: S=W-W2/ W-W1= M/M1-M2 Homework Equations The Attempt at a Solution
  4. M

    Help with deriving transfer function of a second order control system

    Homework Statement Please see attachment for block diagram of the system. Starting with the block diagram given in Figure 2 derive an expression for the overall transfer function of the system, where Gc(s) is in the form given by Eq. (1). Show that the system is a Second Order system...
  5. B

    How can the heat equation be derived for a long circular cylinder?

    Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^{2}+y^{2}} is the cylindrical coordinate. From the three dimensional heat equation derive the equation u_{t}=k(u_{rr}+\frac{u_{r}}{r}). My...
  6. S

    Deriving the Decay Rate Function from Mass & Time Graphs

    Hi. We are given a table containing values of mass(m) and time(t). We have been asked to plot graphs of (m) against (t) and then log(m) against (t). The question is: FROM YOUR GRAPHS, DETERMINE THE FUNCTION FOR THE RATE OF DECAY. Of course i know the formula but have no clue how to...
  7. R

    Deriving t=T/√(1-v²/c²) in Special Relativity | Patent-Invent

    On this page http://www.patent-invent.com/electricity/inventions/special_relativity_1.html you are given that in a certain scenario -(cT)2 = (vt)2 - (ct)2 then it says Hence: t=\frac{T}{\sqrt{1-v^{2}/c^{2}}} But this doesn't rearrange to that equation, and I don't like taking formulae...
  8. L

    How Do You Calculate Group Velocity from Phase Velocity?

    Homework Statement The phase velocity of ocean waves is \sqrt{\frac{g\lambda}{2\pi}} , where g is 9.8 m/s2. What is the group velocity?2. Homework Equations v_{p} = \omega/k v_{g} = \partial\omega/\partial kThe Attempt at a SolutionSo I've been trying to find omega and k from the equation in...
  9. C

    Deriving Projectile Motion Equations from Initial Conditions

    Homework Statement Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them. Homework Equations...
  10. C

    Deriving Projectile Motion Equations

    Homework Statement Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them. Homework Equations...
  11. H

    Deriving Helmholtz Thermodynamic Potential & Corresponding Maxwell Relation

    Homework Statement To state the differential form of the Helmholtz thermodynamic potential and derive the corresponding Maxwell's relation. Homework Equations Stated within the solution attempt. The Attempt at a Solution Helmholtz function: F = U - TS Calculating the...
  12. Saladsamurai

    Deriving 1D Stress Field in a Bar

    So in one of my classes, we very non-rigorously derived the 1D stress field for a bar with a longitudinal surface loading T(x) like show below: By taking out a differential element (assuming constant cross-sectional area) and applying good old Newton's Second, we end up with: A...
  13. A

    Vibrations problem - Deriving the natural frequencies

    Homework Statement A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions...
  14. S

    Deriving the effective potential due to screening

    Homework Statement I'm supposed to show that the Lindhard dielectric functions gives a contribution to the effective potential of a metals as U_{eff}( \vec{r} ) \propto \frac{cos( 2 k_{F}r)}{r^{3}} in the limit of r\rightarrow\infty for d = 3 (3 dimensions) Homework Equations...
  15. S

    Deriving Coulomb's Law: Exploring Virtual Photon Exchange Theory

    derive Coulombs law of electrostatic force by using virtual photon exchange theory of electrostatic field
  16. D

    Deriving Mechanics Equations for the Moon

    Alright, so I have a few questions. a) Consider a moon of mass m orbiting a planet of mass M in an elliptical orbit. The equation for the radius of an elliptical orbit is r=a(1-e2) / (1+ecos\vartheta). Derive equations for the orbital radius of the moon when it closest to and farthest from the...
  17. H

    Did I do this right or get lucky? Deriving spherical shell moment of inertia

    Homework Statement Basically just to find moment of inertia of a spherical shell Homework Equations Moment of Inertia = Int(r^2 dm) The Attempt at a Solution I am in 12th grade and don't know much about integrals? Did I get lucky or am I right? I = Int(r^2dM) dM= (phi)(dA)...
  18. majormuss

    Projectile motion- Deriving the right formular

    Homework Statement Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. Approximately how...
  19. I

    Deriving the Witch of Agnesi Curve

    Hello, I have encountered an exercise in my differential geometry book: to derive the parametrisation and the cartesian equation of the curve witch of Agnesi. To see how it is constructed please see: http://en.wikipedia.org/wiki/Witch_of_Agnesi" How would one derive the results? I am...
  20. B

    Projectile motion, deriving equation

    Homework Statement Derive equations (5) and (6). Calculate at what angles the time and range are maximized. (5) t= ((2 * Vo) / g) * sin\theta (6) Range = x1-xo = ((2 * Vo)/g)(sin\theta)(cos\theta)= (Vo^2/g)(sin2\theta) sorry about the confusing format. I'm new to latex and new to this...
  21. A

    Deriving the Pendulum Time Period Formula from "Fundamentals of Physics

    In the book "Fundamentals of Physics" by H D Young and Freedman,there is formula about the time period of simple pendulum which uses sine function in a complex way which i think is obtained by series expansion of sine function either by Maclurin or Tayler series. Can anyone please tell me how...
  22. K

    Help deriving integer sequence formula

    Hi I'm playing around with partitions and have come up with an integer sequence representing the maximum number of partitions of various "widths" that display the following properties: - min values in partition are equal - max values in partition are equal - partitions contain equal number of...
  23. O

    Deriving Nonrelativistic Euler Equations from Stress Energy Tensor

    Hi, I would like to start from the stress energy tensor for the perfect fluid: T^{\mu\nu}=\begin{pmatrix} \rho c^2 & 0 & 0 & 0\cr 0 & p & 0 & 0\cr 0 & 0 & p & 0\cr 0 & 0 & 0 & p\cr\end{pmatrix} where \rho is the mass density and p is the pressure, and I would like to derive the...
  24. M

    Deriving Equations of Motion for Compound Pendulum with 3 DOF

    Can anyone help? I have to derive eq of motion of a compound pendulum with 3 rotational dof. I know how to do it, for simple pendulum (using Lagrangian's).
  25. B

    Deriving the Formula for Gravitational Potential Energy

    Hey guys, Do any of you happen to know how to derive the formula for General gravitational potential energy (not the mgh one) without using calculus? Thanks. Just in case you guys want to know, I'm trying to derive the equation for this: http://xkcd.com/681_large/. I've got most of it, but I...
  26. T

    Deriving time peroid of a spring

    Hi all, I was wondering if we could go through how we get the time peroid for a spring with a mass m attached to it. The time period is: T = 2pi sqrt(m/k)We know that F = -kx We know the the the acceleration of a spring is always towards the equilibrium point the speed can be measured negative...
  27. T

    Deriving Formula: f2 Frequency of Moving Object

    Homework Statement This is my first post, so it might not be that great... Anyways, I need help deriving the formula. This formula is pertaining to the doppler effect, and more specifically, to find the frequency of a sound made from an object moving toward/away from you. f2= f1(v/v-vs) or...
  28. K

    Astrophysics: Deriving Newton's Gravitational Formula from Kepler's

    Homework Statement Dervie Newton's form of Kepler's third law. decrribing the orbital motion of two stars in circular orbits with masses M1 and M2, separation a, and period P ie. Obtain F=\frac{ G M1 M2 }{ a^2 } From M1+M2=\frac{4 \pi^2 a^3 }{GP^2} Homework Equations Centre of mass...
  29. E

    How can I use theorems to derive a statement about inequalities?

    By using appropriate theorems derive the following statement : a^2 + b^2 + c^2\geq ab + bc +ac
  30. F

    Deriving equaions for harmonic oscillations

    Homework Statement Suppose a particle of mass 0.240 kg acted on by a spring undergoes simple harmonic motion. We observe that the particle oscillates between x = 0.200 m and x = - 0.200 m and that the period of the oscillation is 1.20 s. At time t = 0, the particle is at x = 0 and has...
  31. B

    Deriving Relations Between Generating Functions via Legendre Transformations

    Homework Statement Problem 9.7(a) of Goldstein, 3rd edition: If each of the four types of generating functions exists for a given canonical transformation, use the Legendre transformations to derive the relations between them. Homework Equations F = F1(q,Q,t) p = partial(F1)/partial(q) P =...
  32. P

    Deriving Kepler's Law: Negative Sign Explained

    hi, I am having trouble understanding what happens to the negative sign when i try to derive keplers law. v=d/t where d is the distance around one orbit, so d=2rpi and t is the time for one orbit in seconds which i will call T so v=2rpi/T now using Ep=-Gm1m2/r Ep is gravitational...
  33. B

    Deriving an Expression for g in Terms of M, m, D, H, and t

    There are two blocks of equal mass M that hang from a massless, frictionless pulley. There is a small square block of mass m sitting on top of one of the blocks. When the block is released, it accelerates downward for a distance H until the block of mass m sitting on tip gets caught by a ring...
  34. K

    Why Does Extracting Density Affect My Moment of Inertia Calculation?

    I'm attempting to derive the moment of inertia for a cylindrical object. I know that I=\int r^2 dm which equals =\int r^2 p dV My question begins here, the derivations I seen pull p out of the integral, which makes sense to do, because in this case it's a constant. p=M/(\pir^2L). So if I...
  35. K

    Deriving expression for k_eff

    See attached file: I would like to show theoretically that the first double spring system is equivalent to the second system with only one spring keff. Then I want to derive an expression for keff in terms of k1 and k2. I think this system is in series and therefore keff =1/k1 +1/k2 but...
  36. H

    Deriving Relativistic Energy Problem

    Homework Statement Taking into account the electrons momentum and relativistic energy prove that W=(m(sub0)^2c^4+p^2c^2)^(1/2) Homework Equations p=(gamma)m(sub0)v; W=(gamma)m(sub0)c^2. The Attempt at a Solution I have tried expanding the relativistic factor...
  37. K

    A seeming contrdiction in deriving wave function for delta function potential

    First of all, let me copy the standard solution from Griffiths, section 2.5, just for the sake of clarity. PotentialV(x) = - \alpha \delta (x) The bound state eigenfunction: \psi (x) = \left\{ \begin{array}{l} B{e^{\kappa x}}{\rm{ (}}x \le 0{\rm{)}} \\ B{e^{ - \kappa x}}{\rm{...
  38. P

    Deriving Diffraction Formula

    Homework Statement Basically there's a question that I'm doing which asks me to show how to derive: n lambda=d sin theta We haven't learned it yet and so how do you do it? Homework Equations n lambda=d sin theta The Attempt at a Solution Not a clue! Thanks!
  39. B

    Help with deriving an Equation from 4 others

    Homework Statement Our teacher assigned us this problem of trying to derive and equation from 4 simpler equations and I just can't seem to get the correct answer so I need some help. a= M1g / (1/2)M2+M1 a= acceleration M1= Mass 1 M2= Mass 2 g= gravity R= radius T= tension I= moment of...
  40. Saladsamurai

    Deriving the Bernoulli EquationFluids

    I am trying to follow along with the text's derivation of the Bernoulli equation and I am a little confused with a particular line. The images show an elemental streamtube control volume (CV) of variable area A(s) and length ds. We assume that though the properties may change with time and...
  41. D

    Deriving Σ sin n using Euler's formula

    Homework Statement I was looking over my notes and there was a part that didn't make sense. It's basically using the Euler's formula (e^{ix}=cos(x)+isin(x)) and the fact that sin(x)=Im(e^{ix}) to find what Σ sin n sums to. It starts out like this: But this part isn't relevant to my...
  42. A

    Deriving the divergence in polar coordinates

    Homework Statement I want to find the divergence operator in polar coordinates (theta and r). I know how to write this operator in cartesian coordinates. The Attempt at a Solution I let F(F1,F2) be a vector field. I calculated the partial derivatives of F1 and F2 with respect to x...
  43. J

    Deriving double-angle formula

    Homework Statement Homework Equations My notes say: Cos(x+a) = CosxCosa - SinxSina The Attempt at a Solution When I differentiated each term (using the product rule twice on the right side) I got: (d/dx) { Sin(x+a) = SinxCosa + CosxSina } . Cos(x+a) = -SinxSina...
  44. D

    Deriving an Thermodynamic Equation of State

    Homework Statement Derive the following: \left(\frac{\partial U}{\partial V}\right)_{T}=T\left(\frac{\partial p}{\partial T}\right)_{V}-p Homework Equations Use the partner equation: \left(\frac{\partial H}{\partial p}\right)_{T}=-T\left(\frac{\partial V}{\partial T}\right)_{p}+V...
  45. W

    Deriving Compatibility Conditions for Differential Equations

    I'm not sure if my thought process is correct. I basically looked at 1-D and 2-D self-adjoint problems to see what conditions were imposed on them, and tried to translate over to this problem. Can somebody tell me if I'm correct? Or at least have the right idea? I have my work linked below to...
  46. K

    Signals and Systems: Deriving differential equation from block diagram

    Homework Statement Consider the block diagram below. Find the differential equation of the system. Homework Equations None, other than understanding how block diagrams work. The Attempt at a Solution My attempt is posted below, as an image. The reason I am having such trouble is...
  47. N

    Deriving the Michelson Interferometer Equation: d_m = (m[lambda])/2

    does anyone know how to derive this equation regarding the Michelson interferometer: d_m = (m[lambda])/2 where d_m is the physical distance of a micrometer division, m is the number of fringes that crosses a screen given some d_m and lambda is the wavelength of the laser used to create the...
  48. E

    Deriving torque from a B field on a magnetic Loop

    Homework Statement A wire ring lies in the xy-plane with its center at the origin. The ring carries a counter clockwise current I. A uniform magnetic fireld B is the the +x direction. There are a few parts to the question (Note: Everything except for I is a vector): 1. show that dL =...
  49. D

    Deriving Equations - Freefall, Velocity

    Homework Statement Given a Height of release (d) and the Total time (T) form hand to floor. Derive general equations for vi, vf, h (in terms of d, T, and g) vi = velocity ball leaves hand vf = velocity of the ball the instant before it strikes the ground h = height of the ceilingknown height...
  50. D

    Deriving the 4th equation of motion

    1. All I need to do is derive the 4th equation of motion being v2= v02+2aD from the second (t=(v-v0)/a) and third (D=1/2at2+v0t). 2. In this case D= (Ending-initial distance) V0= Initial Veolocity 3. By having the second equation solved for t I could substitute it in an completely eliminate time...
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