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. B

    Need help deriving an expression for dy/dt

    Homework Statement I need help finding the appropriate expression to use to add a "new calculated column" to produce a vertical velocity vs time graph in Logger Pro. The lab consisted of a ball tied to a rope, creating a pendulum. The Go! Motion sensor was set up to record the oscillations. The...
  2. Pushoam

    Deriving the potential energy of a dipole

    Homework Statement Homework EquationsThe Attempt at a Solution In case of uniform E, torque ##\vec N = \vec p \times \vec E \\ U = \int_0 ^ \theta N d \theta = pE \int_0 ^ \theta \sin \theta d \theta = - pE \cos \theta \text { Here, I assumed that the direction of } \vec N ~ and ~ \vec d...
  3. fisher garry

    A Deriving total energy in a Hydrogen molecule

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  4. fisher garry

    Deriving Larmor frequency problem

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  5. Pushoam

    Deriving equation of wave motion

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  6. P

    I Deriving the E Cross B Drift Velocity: A Puzzling Explanation

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  7. Arisylia

    Deriving the moment of inertia of solid sphere

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  8. T

    Deriving the ionization energy of a hydrogen atom

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  9. S

    A Deriving the Poincare patch from global coordinates in AdS##_{3}##

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  10. redtree

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  11. J

    Deriving expression for potential of a point charge

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  12. binbagsss

    Deriving Wien's Displacement Law

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  13. Tbonewillsone

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  14. mabelw

    Deriving functions relating to condition numbers

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  15. Mr Davis 97

    Deriving the sum of sin and cos formula

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  16. S

    A Deriving matrix element from Lagrangian

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  17. J

    I Question about deriving E=mc^2

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  18. redtree

    A Deriving the Lagrangian from the Hamiltonian operator

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  19. T

    Deriving an expression for the energy required to separate charges

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  20. Vitani11

    Deriving the moment of inertia of a sphere

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  21. A

    I Different methods of deriving the energy-momentum equation

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  22. I

    Kinematics, deriving equations.

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  23. F

    Deriving Magnostatics equations from steady currents

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  24. ATY

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  25. Nikhil Rajagopalan

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  26. J

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  27. R

    I Why is the first term zero in the Virial Theorem derivation?

    Hello everyone! I am reviewing the derivation of the Virial Theorem from an introductory Astrophysics book (Carroll and Ostlie's) and found a step I couldn't follow. I've attached a photo of the step. Can anyone explain how Newton's Third Law brings about eqn 2.41? I don't see how that first...
  28. K

    MHB Deriving expressions using double angle formula?

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  29. J

    I Deriving distances from reference frames

    Hello, I have a question regarding the following picture: Here, person B is moving in his S’ reference frame with a speed of u relative to Person A, who is in his reference frame S. An event shown by a star (*) happens after tA time according to A. The distance of that event is a distance...
  30. binbagsss

    Deriving continuity equation of phase space in Statistical Mechanics

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  31. binbagsss

    Real scalar field , Action, variation, deriving EoM

    ## L(x) = L(\phi(x), \partial_{u} \phi (x) ) = -1/2 (m^{2} \phi ^{2}(x) + \partial_{u} \phi(x) \partial^{u} \phi (x))## , the Lagrange density. ## S= \int d^{4}(x) L (x) ##, the action. ## \phi -> \phi + \delta \phi ## (just shortened the notation and dropped the x dependence) I have ##...
  32. F

    I Deriving the volume of a sphere using semi-circles

    Apologies if this question has already been asked, but is it not possible to derive the formula of a sphere by imagining a circle sliced in two, then rotating this semi-circle about the flat side (imagine the flat side is stuck to a skewer) by 2Pi, so as to sum up the semi-circles to "create"...
  33. R

    I Derive Convolution Expression for Z_PDF(z)

    Hi Can I derive the expression for Z_PDF(z) where: Z = t(X,Y) = X + Y By starting with: Z_PDF(z)*|dz| = X_PDF(x)*|dx| * Y_PDF(y)*|dy| Z_PDF(z) = X_PDF(x) * Y_PDF(y) * |dx|*|dy|/|dz| and then substitute the deltas with derivatives and x and y with expressions of z?
  34. tomwilliam2

    Deriving equations of motion for restricted 3-body problem

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  35. Mr Davis 97

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  36. R

    Need Help Deriving Projectile Motion Equations

    Could someone please assist me in deriving the following projectile motion equations from the following kinematics equations? Kinematics Equations: Δx = v0xt + ½at2 ; Δy = v0yt + ½at2 vx = v0x + at ; vy = v0y + at Δx = ½(v0x + vx)t ; Δy = ½(v0y + vy)t vx2 = v0x2 + 2aΔx ; vy2 = v0y2 + 2aΔy...
  37. jdawg

    Deriving hydrostatic pressure equation for an ideal gas

    Assume: Hydrostatic Situation, ideal gas Use empirical formula T = T0 - Bz I have rechecked my work several times and can't seem to find a mistake. The answer is supposed to be: p2 = p1((T0 - Bz)/T0)(g/Bz) dp/dz = -ρg Now substitute ideal gas equation for ρ dp = -(p/RT)g dz ∫(1/p) dp...
  38. K

    I Deriving expression as a function of another variable

    I am attempting to understand how I can derive a new expression as a function of another variable in this existing expression. This is a college undergraduate course but I can't recall doing this much before, maybe in high school. I have taken all the way up to ODE's and PDE's. The confusion...
  39. A

    B Deriving the gravitational constant factor for lbf

    I have never had to use the English Engineering System so I am having a bit of a struggle here. I understand the concept of an inconsistent system of units. I understand the following 2 statements: 1lbf = 1lbm x 32 ft/sec^2 1lbf = 1slug x 1 ft/sec^2 When given a problem that is asking for the...
  40. tomwilliam2

    Two body problem, deriving energy expression

    Homework Statement This problem relates to the two body problem of two rotating point masses, where one is much larger than the other. Equate the orbital energy per unit mass ##\epsilon## with the moments of momenta at the apses to get: ##\epsilon = -\mu/2a## Homework Equations The orbital...
  41. Mr Davis 97

    B Deriving law of sines from cross product

    I am trying to derive the law of signs from the cross product. First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...
  42. M

    Deriving the thermodynamic beta from Lagrange Multipliers

    I'm nearly at the end of this derivation but totally stuck so I'd appreciate a nudge in the right direction Consider a set of N identical but distinguishable particles in a system of energy E. These particles are to be placed in energy levels ##E_i## for ##i = 1, 2 .. r##. Assume that we have...
  43. G

    Deriving the formula for a magnetic dipole field

    Hello PF! I am trying to find out how the formula for the magnetic field of a dipole magnet is derived, so far I've delved into maxwell equations, but I am finding the math too complicated to read. My state's education system is very far behind, and I am not accustomed to characters and symbols...
  44. Erenjaeger

    Deriving to find speed (angular motion)

    Homework Statement Going through a lecture recording from a lecture I missed the lecturer says "to get the relationship between translational speeds and angular velocities we will take a differential" what is that relationship she is talking about? does she mean converting between the two? The...
  45. rezkyputra

    Deriving Einstein Eq. from Variational Principle

    Homework Statement Okay, in Carrol's Intro to Spacetime and Geometry, Chapter 4, Eq. 4.63 to 4.65 require a derivation of a difference between Christoffel Symbol. I did the calculation and found my answer to be somewhat correct in form, but the indices doesn't match up Homework Equations So...
  46. P

    I Deriving EM Energy Conservation from Lagrangian

    I'm trying to derive the conservaton of energy for electromagnetic fields with currents from the action principle, but I have some trouble understanding how the interaction term in the Lagrangian fits into this. The approach I have seen so far has been to express the Lagrangian density as...
  47. J

    I Deriving maximum velocity in a rotated frame

    I have a particle that travels in the cartesian plane with the maximum velocity of A units along the x-axis and B units along the y-axis per unit of time. How do I go about deriving the maximum velocity of my particle in the rotated uv plane? (the maximum distance the particle can along the u...
  48. R

    Deriving Strain in Cantilever Beam with Known Deflection

    I am trying to derive the strain at the base of a cantilever beam with a known deflection. I know the bending stress is equal to Mc/I, so the strain is Mc/IE, where c is the distance from the neutral axis. For a point load ,P, the strain would then be PL/IE. Since the deflection is known I...
  49. V

    B Deriving Electron Wave Function from Hole Wave Function

    Assume that i have a wave function of holes in a solid, can we derive the wave function of electrons? If can then how?
  50. J

    How can the 0.5 in the acceleration and distance formula be explained?

    Hello all, First of all I want to let you know that my question is very basic and that it involves discrete changes in velocity due to acceleration for every given Δt. I was trying to derive the relationship between the distance and acceleration in a formula and here's what I came up with: 1...
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