What is Unit: Definition and 1000 Discussions

UNIT is a fictional military organisation from the British science fiction television series Doctor Who and its spin-off series Torchwood and The Sarah Jane Adventures. Operating under the auspices of the United Nations and initially led by Brigadier Lethbridge-Stewart, its purpose is to investigate and combat paranormal and extraterrestrial threats to Earth. Several UNIT personnel (such as the Brigadier, Sergeant Benton and Mike Yates) played a major role in the original Doctor Who series, and it was a regular feature from The Invasion (1968) until The Seeds of Doom (1976).
Originally referred to as the United Nations Intelligence Taskforce, executive producer Russell T Davies said in 2005 that the UN was no longer happy to be associated with the fictional organisation and the UN's full name could now no longer be used. However, the "UNIT" and "UN" abbreviations could be used as long as it was not explained what the letters stood for. In 2008, he announced that the organisation's name had been changed to the Unified Intelligence Taskforce. This new name was first mentioned on-screen in "The Sontaran Stratagem", also in 2008, in which it was indicated in a line of dialogue that the United Nations still supports UNIT with funding.

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  1. deedsy

    Unit Conversion - Flux Densities

    Homework Statement I need to convert from a fv in units of Jy to fλ in units of erg s^-1 cm ^-2 A^-1 fv = 1.0254e-2 Jy Homework Equations fv dv = fλ dλ fλ = fv dv/dλ and because v = c/λ... fλ = fv*c / λ^2 Also 1 Jy = 10^-23 erg cm^-2 s^-1 Hz ^-1 The Attempt at a Solution...
  2. M

    Unit Conversions Grams to Watts

    Homework Statement The power available (output) is measured by the velocity at which you are moving and the thrust required to create that movement. NOTE: Conversions for proper units are provided below equation. Power Available: Pout = Tc * v where: Pout = power available (watts) Tc...
  3. C

    Magnitude, Unit vectors,unknown variables

    Homework Statement a and b are vectors in R^3 s.t. a=(1,7,-4) and b= -3j-4k 1. Find ||3a-3b|| (magnitude of 3a-3b) 2. Find unit vector u in direction of 3a-3b, write answer in form (u1,u2,u3) 3. Find vector of length 8 in direction of a (write answer in form "-") Homework Equations...
  4. A

    Simple Unit Analysis for Generator Revenue Calculation

    Homework Statement $$Let\quad n\quad =\quad the\quad number\quad of\quad hours\quad I\quad run\quad a\quad 40\quad kilowatt\quad generator.\\ Assume\quad that\quad it\quad costs\quad $0.08\quad for\quad 1\quad kWh.\\ Revenue\quad from\quad generator=\frac { $0.08 }{ kW\cdot hours } \quad...
  5. A

    Cross products for unit vectors in other coordinate systems

    I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...
  6. J

    What is the difference between unit vectors v and r?

    Follow the 1st ideia: \\ d\vec{r} = dr \hat{r} + r d\theta \hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \frac{dr}{dr} \hat{r} + r \frac{d\theta}{dr}\hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \hat{r} and now: \\ \frac{d\vec{r}}{dr} = \frac{d\vec{r}}{dt} \frac{dt}{dr} = \frac{d\vec{r}}{dt}...
  7. K

    Unit vector tangent to the surface

    I have the following question: Given that ø = (x^2)y + cos(z) find the unit vector n which is both tangent to the surface of constant ø at (1,1,∏/2) and normal to the vector b = x + y - 2z (where x y and z are the unit vectors) I have calculated ∇ø = 2x + y - z (again where x y and z are...
  8. S

    Reactions of a redundant frame structure using Unit Load Method

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  9. ThomasMagnus

    Which Atmosphere Unit Should I Use for Lab Calculations: Technical or Standard?

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  10. U

    Evaluating and integral including unit step function

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  11. JasonHathaway

    Unit vector in cylindrical coordinates

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  12. T

    What is measurement unit of digital clear sound for devices

    like for example digital unit measurement for clear images in devices is ...pixel
  13. JasonHathaway

    Understanding Unit Vectors: A Step-by-Step Guide

    Hi everyone, Just want to know how does the the unit vector become in that form: \vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{x \vec{i}+y \vec{j}}{4}
  14. B

    Laplace Transform for shifted Unit Step Function

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  15. E

    Derivation of Phi-Hat wrt Phi in Spherical Unit Vectors

    Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've...
  16. Z

    Finding perpendicular unit vector using inner product

    Homework Statement You are given that with x = (x1,x2), y = (y1,y2), the formula (x,y) = [x1 x2] [2 1;1 2] [y1;y2] (where ; represents a new row). is a inner product for the vectors in R2 Using this inner product, find a unit vector perpendicular to the vector (1,1) Homework Equations The...
  17. T

    Generating randomly oriented non-intersecting cylinders in a unit cell

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  18. S

    Dyadic Squares in the Unit Disc: A Proof and Critique

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  19. O

    Can the volume of primitive unit cell and unit cell be different?

    Hi all, I read The unit cell is the smallest structure that repeats itself by translation through the crystal. Some says premitive unit cells contains atoms only at the corners while a unit cell may contain extra atoms in between(like bcc or fcc). At one place I found this: For each...
  20. S

    How to interpret this problem involving dyadic squares and unit disc?

    The following problem is from the textbook "Real Mathematical Analysis" by Charles Chapman Pugh. Given ##\epsilon > 0##, show that the unit disc contains finitely many dyadic squares whose total area exceeds ##\pi - \epsilon##, and which intersect each other only along their boundaries. I...
  21. B

    Why does Sin represent Y on unit circle

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  22. T

    How Does Doting a Unit Vector With a Vector A Affect the Result?

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  23. Ascendant78

    Finding a curve's unit tangent vector

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  24. ThomasMagnus

    Integrating Velocity When in Unit Vector Notation

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  25. T

    What Is the Dot Product of Two Parallel Unit Vectors?

    Homework Statement The dot product for two.parralel pointing.unit.vectors is ? A. 1 B. 0 C. -1 D. Undefined [b]2. Relevant equation The Attempt at a Solutionsince they are unit vectors they have a magnitude of 1,this implies that the dot product is 1,since the angle between...
  26. N

    What Does Higher Permittivity Substrates Mean for Unit-to-Wavelength Ratio?

    hi friends, can anybody clear my concept about the following sentence. " if we use substrates with higher permittivity, like quartz or GaAs that has been used in previous successful experiments, the unit cell will have smaller unit-to-wavelength ratio".
  27. J

    Derivative of Unit Vector in a Rotating Frame

    Before anyone thinks I didn't numerous attempts before opening this topic, take a look at my rough draft of mathematics in the annex. So, a simple question. How derivate an unit vector wrt any variable? I can derivate any unit vector wrt θ or φ, obivious, but how derivate the vector φ wrt to x...
  28. A

    How do I calculate the number of collisions per unit area in an ideal gas?

    I an ideal gas how do I calculate the number of collision per unit area? By collision I do not mean collision between the atoms but rather it is a problem where I know that a nucleation cluster of area A is in my gas, and I want to find the probability that it will get hit by an atom. I know the...
  29. tipu_sultan

    What is role of Quad Ring Main Unit (QRM) in Substation?

    Below is the typical diagram of a Substation in which MIL and MIR are with TR-1 and TR-2 respectively. Where TR-1 and TR-2 are the transformers whose function is to step down the voltage. I have also confusion about the flow(path) of the electricity with in substation. The confusion is that...
  30. M

    Derivative of a unit vector

    Homework Statement the first derivative of a vector of constant magnitude is the cross product of the angular velocity of the vector(i.e , the angular velocity of the moving coordinate system ) and the vector itself.)Homework Equations di/dt= w x i , here w is the angular velocity and x is...
  31. jdawg

    What's the Difference Between Ax and i-Hat in Vector Notation?

    Homework Statement So this isn't really a specific homework question, it's more of a general one. What is the difference between ax and i(hat)? I thought they were the same thing. Can someone please explain the difference? Homework Equations The Attempt at a Solution
  32. jdawg

    Unit conversion with density of gold

    Homework Statement Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 4.713 g, is pressed into a leaf of 6.549 μm thickness, what is the area of the leaf? (b) If...
  33. J

    Cross product between unit vectos

    I have a nice table that shows the dot product between unit vectos (see annex). I'd like know how is the cross product between unit vectos of all basis. Do you have a table with such information?
  34. N

    Determining unit vector of acceleration and velocity in circular motio

    As a particle orbits around a circle, the unit vector of the velocity and acceleration component is constantly changing, so, how do I determine the unit vector?
  35. U

    Average and variance of a unit sphere

    Homework Statement Consider the sphere x2 + y2 + z2 = 1 Find the mean and variance. Homework Equations The Attempt at a Solution Mean = 0 (Symmetry) Variance Probability = \frac {dV}{\frac{4}{3} \pi R^3} = \frac {4 \pi r^2 dr}{\frac{4}{3} \pi R^3} = 3 \frac {r^2}{R^3} dr Variance =...
  36. G

    Is \(\frac{\partial}{\partial \phi}\) a Killing Vector on the Unit Sphere?

    \bar{}Homework Statement Hi, I want to show that \frac{\partial}{\partial \phi} is a Killing vector on the unit sphere with metric ds^2 = d\theta^2 + \sin^2 \theta d \phi^2 Homework Equations I compute the Christoffel symbols to be \Gamma^\theta_{\phi \phi} = -\sin \theta \cos...
  37. Ascendant78

    Understanding Vectors vs Unit Vectors: Differences and Uses in Physics

    I am a bit confused about what the difference is between the two? To give some specific context where it has thrown me off, say if I were to define a charge with a vector r and compared that to a unit vector r hat, what exactly is the difference between what each of those tells me? I have...
  38. P

    MHB Unit sum composed of unit fractions

    Is it necessary for a unit sum composed of unit fractions to include 1/2? Doing maple runs this seems to be the case, but it is not evident to me how this could be Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia But...
  39. R

    How to Convert J/K and kgJs/m into m/s?

    Dear All, J/K into m/s ? Or kgJs/m into kg? thanks for your help! Rajini.
  40. A

    Algebra with Complex Numbers & Imaginary Unit

    When i is defined by an equation which has 2 solutions, how does it make sense to do algebra with complex numbers?
  41. H

    Determinant of a unit columns matrix

    If all columns of a matrix are unit vectors, the determinant of the matrix is less or equal 1 I am trying to prove this assertion,which i guess to be true. can anybody help me? Thank's in advance
  42. J

    Does the curvature of spacetime have a unit?

    Does the curvature of spacetime have a unit?
  43. Q

    How to Calculate the Density of Aluminum in a Face-Centered Cubic Unit Cell

    (Skip to the bottom for my questions). I'm just sounding off my thoughts above. Homework Statement Find the density of aluminum, which crystallizes in a face-centered cubic unit cell. The atomic radius is 143 pm. Homework Equations edge length of FCC is (4/sqrt2)r. The Attempt at a...
  44. skate_nerd

    MHB Showing relationship between cartesian and spherical unit vectors

    I am asked to show that when \(\hat{e_r}\), \(\hat{e_\theta}\), and \(\hat{e_\phi}\) are unit vectors in spherical coordinates, that the cartesian unit vectors $$\hat{i} = \sin{\phi}\cos{\theta}\hat{e_r} + \cos{\phi}\cos{\theta}\hat{e_\phi} - \sin{\theta}\hat{e_\theta}$$ $$\hat{j} =...
  45. F

    Scaled unit impulse/step sequences

    Homework Statement b_{k} = {4, 1, 1, 4} x[n] = 2u[n] Write your answer using scaled unit impulse sequences and scaled unit step sequences. Write explicitly. Homework Equations The Attempt at a Solution 4114 2222222... ------------ 8228 8228 8228 8228 8228 ... ------------...
  46. L

    Curl in spherical coords with seeming cartesian unit vector

    Homework Statement I have a problem that is the curl of jln(rsinθ) Since this is in spherical, why is there a bold j in the problem? Doesn't that indicate it's a unit vector in cartesian coordinates? Can I do the curl in spherical coordinates when I have a cartesian unit vector in the...
  47. Raerin

    MHB If a and b are unit vectors....

    If a and b are unit vectors and |a + b| = sqrt(2). What is the value (dot product) of (2a-b).(a+3b)? Is the answer -1 by any chance? If not... I know how to find the dot product and find the magnitude and add vectors, etc. but I have never came across this a question before. I am very unclear...
  48. F

    Matrix transformations and effects on the unit square

    I was looking over my notes today, and I realized that there was a point that isn't pretty clear. If we have the image under T (being T a matrix transformation induced by a matrix A) of the unit square, then its area should be abs(det(A)). Why is this though? I was looking at the proof and I...
  49. Rapier

    Laplace Transforms with an Undamped Spring with Unit Impulse

    Ok, so I start out with the basics and find k. F=ma=kx (1.5 kg)(9.8 m/s^2) = k (4.9 m) k = 3 N/m I also know from the problem that c=0 (no damping) and x(0) = 2m and x'(0) = 0. ƩF = ma ma = -cx' - kx, a = x'' mx'' + cx' + kx = 0 and since c=0 mx'' + kx = 0 Nothing out of the...
  50. B

    Calculation of work involving unit vectors

    Homework Statement A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j How much work does the force you apply do on the grocery cart? Homework Equations...
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