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. N

    Deriving the number of stars as a function of flux and bolometric magnitude.

    QUESTION A star of bolometric luminosity L at a distance r will exhibit a bolometric energy flux F given by F = L/4πr2 in the absence of obscurity. A. Assume that all stars have the same bolometric luminosity L and that stars are uniformly distributed in space with a number density n...
  2. R

    Deriving addition of sines from Euler's formula

    Deriving addition of sines from Euler's formula (edit: please ignore) Homework Statement I'd like to derive the value of sin(2πkt + θ) so that I can convince myself that the Fourier sum in terms of sines and cosines works. I found the derivation on Wolfram by using the full Euler's formula...
  3. G

    Deriving the duffing equation?

    Say I have a mass m on a non linear spring k with some damping b. I start with the restoring force of the spring F=-kx+x^3... the x^3 is the non linearity. Set that equal to Newtons second law F=mx'' = -kx+x^3 Add in the damping which is dependent of velocity bx' ......mx'' = -kx +...
  4. P

    Understanding the Derivation of the Dirac Equation in Cosmology

    Hi i am trying to derive the Dirac equation of the form: [i\gamma^0 \partial_0 + i\frac{1}{a(t)}\gamma.\nabla +i\frac{3}{2}(\frac{\dot{a}}{a})\gamma^0 - (m+h\phi)]\psi where a is the scale factor for expnasion of the universe. I understand that the matter action is S=\int d^{4}x e...
  5. A

    Deriving the Correction Factor for Non-Ideal Spring Frequency Equation

    Homework Statement In general, I know that you can use the equation ωn=[k/m]^0.5 to calculate the natural frequency of a hanging spring and mass system. However, for a non-ideal spring (where the mass of the spring isn't negligible) a correction factor is added to the equation and it...
  6. S

    Optics; Deriving the index of refraction from Snell's law

    Homework Statement There is a diagram in the problem statement so here is a link to the image of the problem: http://imgur.com/KDrRsyO Homework Equations Snell's Law: n_{1} * sin(\theta_{1}) = n_{2} * sin(\theta_{2}) The Attempt at a Solution My attempt using Snell's law...
  7. P

    Tips for deriving the friedmann equations

    Hi I am using the metric ds^{2}=c^{2}dt^{2}-a^{2}(t)[\frac{dr^{2}}{1-kr^{2}}+r^{2}(dθ^{2} + sin^2θd^{2}∅)] and am subsequently trying to derive the christoffel symbols: \Gamma^{\sigma}_{\mu\nu}=\frac{1}{2}g^{\sigma\rho}(\partial_{\nu}g_{\rho\mu} +\partial_{\mu}g_{\rho\nu}...
  8. S

    Discontinuity Waves: Deriving the expressions

    Homework Statement A long string of linear mass density μ_1 = 1.0 gr/cm is joined to a long string of linear mass density μ_2 = 4.0 gr/cm and the combination is held under constant tension. A transverse sinusoidal wave of amplitude A _i = 3.0 cm and wavelength λ =25 cm is launched...
  9. C

    Deriving equation for minimum height in projectile motion with two give me's

    deriving equation for minimum height in projectile motion with two give me's :) Homework Statement A ball is launched at a 45 degree angle and lands 152.4 m away. What is the maximum height the ball will reach during its flight. I Know the answer, what I need is to find a way to derive an...
  10. R

    Problem deriving failure of simultaneity at a distance

    Problem deriving "failure of simultaneity at a distance" Homework Statement I'm trying to derive the failure of simultaneity at a distance from the spatial part of the Lorentz transformation. In his treatment of the subject, Feynman glosses over the algebra/derivation and produces the...
  11. G

    Issue with deriving the Lorentz Factor

    Hello, I've seen several derivations of it and I understand them, specially the one in two dimensions with the right angled triangle, but when I try it in 1 dimension, I always find that the condition that the speed of light is the same in all the inertial frames, isn't enough to specify what...
  12. A

    Deriving tangent plane equation - assuming 'c' is non-zero

    In Stewart's calculus text, the way he derives the tangent plane equation at some point is to divide the general plane equation a(x-x_0)+b(y-y_0)+c(z-z_0)=0 by c This must mean c is always non-zero right? But isn't c is the 'z'-component of the normal vector to the surface at some point...
  13. T

    Deriving the London's equation for superconductor

    The equation can be obtained from the fact that the "canonical momentum of the ground grstate of superconductor is zero", but where does this fact follow from. P.S. Jackson gives a vague reference to Kittel, which I couldn't find in his Introduction_to_solid_state/Quantum_theory_of_Solids.
  14. A

    Deriving the Metric from the Energy-Momentum Tensor

    Say we were given an expression for the energy-momentum tensor (also assuming a perfect fluid), without getting into an expression with multiple derivatives of the metric, are there any cases where it would be possible to deduce the form of the metric?
  15. 7

    Deriving a Minkowski Force Matrix: Exploring 4-force

    Our professor derived a Minkowski force like this: F^\mu = \left[ \gamma(e\vec{E} + e(\vec{v}\times \vec{B})) , \gamma \frac{e \vec{E} \vec{v}}{c} \right] Does this mean that i can write 4-force like this? F^\mu = \begin{bmatrix} \gamma(e\vec{E} + e(\vec{v_x}\times \vec{B}))\\...
  16. S

    Deriving Rocket's position from acceleration.

    Homework Statement There's a short introduction saying that honing missiles can determine their position by utilizing their acceleration, then the problem says: Suppose that the missile's acceleration obeys the following equations: \\ a_x = 0.8\\ a_y = -6.0 - 3.0t Knowing that, in t =...
  17. S

    Deriving position from a car's velocity equation.

    Homework Statement A driver sees the red light, and instead of braking the car, changes the gear to neutral. Suppose that velocity obeys this equation: v = v_0 * e^{-bt} Where v_o = 20 m/s and b = 0.150 s^{-1} a)Acceleration when time equals 0;(Answer:-3.0 m/s^2) b)Displacement when t=5.0...
  18. C

    Deriving Expression for Population Fraction (Statistical Mechanics)

    Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...
  19. G

    Memorising formulas or deriving them?

    Hello, I'm new here and this is the first thing I ever write on this forum, hence the question if this is the wrong place to post anything remains unanswered on my part. I came across this forum doing something on the internet, I can't remember what. I'm certain though that it was related...
  20. A

    Deriving the equation of a tangent plane

    I am trying to derive the equation of a tangent plane at some point (x_0, y_0) on a surface using vectors. This is how I have been trying to do it: The tangent line at (x_0, y_0) in the x-direction is z=z_0+f_x(x-x_0) so the vector parallel to it is L_1=<(x-x_0), 0, (z-z_0)>. Similarly...
  21. MarkFL

    MHB Two methods for deriving the quadratic formula that I was not taught in school

    As a student, I was taught 3 ways to solve quadratic equations: i) Factoring ii) Completing the square iii) Applying the quadratic formula, derived by completing the square on the general quadratic in standard form: (1) $\displaystyle ax^2+bx+c=0$ To complete the square, I was taught to...
  22. A

    Deriving the algebraic definition the dot product

    Is there a way of deriving the algebraic definition of the dot product from the geometric definition without using the law of cosines?
  23. G

    Deriving the equation of points for exact fitting and shape analysis

    Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...
  24. C

    Deriving the solution for a free particle from the TISE

    Homework Statement In my physics course, we have been given 'plausibility' arguments for the solutions of the time dependent/time independent SE. However, have done a Calculus course alongside, I feel I should really derive these solutions, since I have learned about the techniques of second...
  25. C

    Deriving relation between angular momentum reduction by torque

    Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial...
  26. Graeme M

    Deriving average surface temperature of a blackbody sphere?

    I have been reading about climate change recently and I have run into a problem understanding the Earth's energy budget. I will try to summarise my question but am happy to try to expand if needed. Bear in mind I am just an interested average Joe with little science background and probably a...
  27. D

    Need help deriving multiple quantities

    Need help differentiating multiple quantities Homework Statement f′(x) = (x − 1)(x − 2)^2(x − 3)^3(x − 4)^4(x − 5)^5 I need help in trying to differentiate this equation. I know could use a combination of the chain and product rule to figure it out, but my teacher said that doing so would...
  28. A

    Need help deriving the general maximum height equation

    Homework Statement You need to derive the general maximum height equation for projectile motion. This equation allows you to calculate the maximum height a projectile reaches or could reach during its motion. Like other such equations we derived in this unit, this one is also very short and...
  29. A

    Deriving charge for Noether current in free complex scalar field QFT

    Homework Statement Hi I a attempting to derive the expression for the conserved Noether charge for a free complex scalar field. The question I have to complete is: " show, by using the mode expansions for the free complex scalar field, that the conserved Noether charge (corresponding to complex...
  30. C

    Deriving Relationships for C_P - C_V & C_F - C_L in Stretched Wires

    Homework Statement I have been stuck on the following question for a while now, particularly part B and C, and I'd like some help with it please. I've completed part A already. The Question: (A) Combine the following TdS equations: TdS = C_{v} dT + T\left(\frac{\partial P}{\partial...
  31. T

    Physics lab; deriving for μs and μk

    1. Physics Lab : Homework Statement design, run and report an experiment to calculate A) μs B) μk between a flat bottomed object and a flat surface ( include a section called "theory" in which you formally derive an expression for μs and μk ) im basically just having troubles deriving ...
  32. C

    Deriving Efficiency of a Diesel Engine Formula

    Homework Statement The Diesel cycle is an idealized representation of the process that occurs in a Diesel combustion engine, as shown in the graph below. Starting at point a, the Diesel cycle consists of an adiabatic compression, an isobaric expansion, and adiabatic expansion and an isochoric...
  33. L

    Help deriving a chi-square confidence interval

    Homework Statement Assume Y1, ... , Yn is a sample of size n from a gamma distributed population with α = 2 and unknown β a) Use the method of moment generating functions to show that U = 2 \sum_1^n Y_i / β is a pivotal quantity and has a chi-square distribution with 4n d.f. b)...
  34. G

    Problem in deriving an expression

    Hi! In this paper: http://www.atm.ox.ac.uk/user/read/mechanics/LA-notes.pdf On the bottom of page no. 25 there is written, that: \int δWdt=-\int δVdt. Why is that? Can anyone explain into me? Thanks in advance.
  35. J

    Deriving expressions for Linear Expansivity and Young's Modulus

    Homework Statement The equation of state of a system consisting of a cylinder of a certain perfectly elastic material, subjected to an axial load F, is F= CT(L-Li)^2 where Li is the unstretched length, L is the length under a load F when the temperature is T on a selected empirical...
  36. M

    Deriving equation from 3D Euler Equations.

    Homework Statement I've got the 3D Euler equations \frac{\delta u}{\delta t} + (u\cdot \nabla)u = -\nabla p \nabla \cdot u = 0 I've been given that the impulse is \gamma = u + \nabla\phi Homework Equations And I need to derive \frac{D\gamma}{Dt} = -(\nabla u)^T \gamma + \nabla...
  37. J

    Deriving Jeans' Mass for Gravitational Collapse

    I need to show that the critical (Jeans') mass for a hydrogen cloud of uniform density to begin gravitational collapse can be expressed as: M=(v^4)/((P^.5)(G^1.5)) Where v is the isothermal sound speed, and P is the pressure associated with the density ρ and temperature T. I don't...
  38. M

    Deriving values from experimental data (algebra help)

    One more question - I'm working on a problem in which I need to determine the values of R and p in the equation: {E_{B} = -RZ^{2}n^{p}} Where Z is 1 (we're using a hydrogen atom), and n is the principle quantum number of the electron. I know p is 2, but the point of the exercise is the...
  39. J

    Can You Derive Equations Using UAM Principles?

    Homework Statement Can you come up with (i.e. derive) equations 5-1 and 5-2 on your own using UAM equations? Try it Homework Equations This is the equation I need to end up at... R=Vox/g(Voy+(Voy^+2gh)^1/2 The Attempt at a Solution I am not really sure where to start. I...
  40. B

    Deriving equation of a ramp function graph.

    Hello, here is my problem. http://imageshack.us/a/img543/827/rampfunction.png I'm having a little trouble coming up with the function f(t). I have something like: f(t) = [(A/T)*t -A] + [(A/T)*(t-2T) -2A] + A*1(t-3T) Am I on the right track here? Thanks!
  41. S

    Projectile Motion- Deriving equation

    Homework Statement Part 1- Derive an algebraic expression for the time-of-flight of a projectile launched with initial speed v0 from a height h at an angle θ above horizontal. (Use any variable or symbol stated above along with the following as necessary: g. Do not substitute numerical...
  42. J

    Deriving Arctan(z) formula using series.

    Hi, I am still trying to learn latex so this might fail but anyway, I am trying to establish the identity arctan(z) = \frac{1}{2i}log(\frac{1+iz}{1-iz}) By using the power series of log(1+iz) and log(1-iz) I have found the power series for both of these functions as well as arctan(z)...
  43. F

    Deriving the major and minor axis of an ellipse

    1. Deriving the major and minor axis of an ellipse from conjugate diameters pointsCurrent solution: double x1 = Diameter1.X - Center.X; double y1 = Diameter1.Y - Center.Y; double x2 = Diameter2.X - Center.X; double y2 = Diameter2.Y - Center.Y; double xc = (x2 + y1) / 2; double yc = (y2 - x1) /...
  44. B

    Trouble Deriving a Constant Acceleration Formula

    Q: How long does it take a car to cross a 30 m-wide intersection after the light turns green, if it accelerates from rest at a constant 2.00 m/s^2? Attempt: V=V0 + at; x-x0/t=v0+at; x-x0=v0+at^2; x=v0+x0+at^2; 30=0+0+2t^2; 15=t^2. The square root of 15 ended up being my final answer, when...
  45. D

    What is the limit of (ah-1)/h as h approaches 0?

    Hey, I am having some difficulties. So it's my understanding that the function ex comes around out of a desire to have a function whose derivative is equal to itself. Well we can show that if f(x)=ax, a>0, then f'(x) is equal to a multiple of itself using the limit definition of the...
  46. K

    Very Stuck on Deriving Projectile Motion Formulas

    Very Stuck on Deriving Projectile Motion Formulas Hey, I need some help :( . I've got an exam next Thursday, and I really suck at this stuff right now. So I need to get better! We are studying kinematics (1d and 2d). In this problem I need help with, we are given the attached diagram...
  47. S

    How correct is deriving Coulomb's Law from Gauss's Law

    How correct is "deriving" Coulomb's Law from Gauss's Law Homework Statement Here is a question that appeared in my school question paper: "Derive Coulomb's Law from Gauss's Law." 2. The attempt at a solution I tried the following: Consider a Gaussian Sphere or radius $r$ By Gass's...
  48. BWV

    Deriving the Propagator: Understanding Zee's Book and the Fourier Transform

    This is more of a math question than a physics one, but following the discussion of the propagator in Zee's book: -(∂2+m2)D(x-y)=δ(x-y) he then gets, by taking the Fourier transform of the Dirac delta and dividing through: D(x-y) = \int\frac{d^4k}{2π^4} \frac{e^{ik(x-y)}}{k^2-m^2+iε}...
  49. S

    Understanding Differentials: Deriving dε = F dot dr

    Homework Statement The proof begins: Suppose that F is conservative. Then a scalar field ε(r) can be defined as the line integral of F from the origin to the point r. So ∫F dot dr = ε(r), where the limits of integration are from 0 to r. The next step, however, eludes me: From the...
  50. D

    Deriving the volume and surface area of a cone

    Hello, this is my first time posting on physics forums, so if I do something wrong, please bear with me :) I am trying to derive the formula for the lateral surface area of a cone by cutting the cone into disks with differential height, and then adding up the lateral areas of all of the...
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