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. R

    Unit conversion mm/sqrt(Hz)/degree to m^2/Hz/rad

    Hello, I have two datasets containing power spectral density data to be compared. One of these datasets is presented in units mm/sqrt (Hz)/degree, and I would like to do some transformation so that data is comparable with the other set, which has units m^2/Hz/rad. Any help on how to do...
  2. J

    Observe a filter response to a unit step?

    Hi guys, what does it mean to observe a filter response to a unit step? The book gives a transfer function and I've recreated it in Proteus ISIS. Now it asks me to simulate a square wave as an input (i used a pulse generator), and then observe a filter response to a unit step, describing the...
  3. I

    Uniform Distribution on unit Circle

    I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...
  4. P

    The space between a unit 'sphere' in n dimensions within an n-dimensional cube

    If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can find is just √2 - 1. Doing a similar thing with a sphere in a cube we get √3 - 1 I've heard the n-dimensional analogue is √n - 1. Which is crazy as it means the gap is bigger...
  5. C

    A/m Unit Explained: Magnetic Fields

    hello, I can't seem to make sense out of amper/meter...one amp flowing throw a wire with a length of 0.5m would be 2A/m ? how does relate to the magnetic field?
  6. L

    Model Dynamics of Unit Mass Sliding Down y=f(x) Under Gravity

    For a unit mass sliding down the stationary curve y = f(x) at the point (x, y), we can consider our mass to be sliding down a stationary inclined plane which is tangential to the curve at the point (x, y). The slope of this inclined plane is thus \frac{dy}{dx}(x). For the remainder of this...
  7. N

    Resnick Halliday Krane Unit Vectors question

    The start of a new school year in Ap physics C, and our favorite engineering professors causing students distress! Maybe the champions of the textbook can help me out... = ) Homework Statement 1. Two vectors are given by a = 4i hat - 3j hat + k hat b = -i hat +j hat + 4k hat. Find a) a + b...
  8. M

    MATLAB Plot unit circle in chebychev metric in MATLAB

    Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this in MATLAB, using the 'pdist' and 'cmdscale' functions. My uber-complex code is the following: clc;clf;clear all; boundaryPlot=1.5; % Euclidean unit circle for i=1:360...
  9. D

    Magnitude of current passing through unit area in atmosphere(He2+ and O2-)

    Homework Statement At a high point in the Earth’s atmosphere, He2+ ions in a concentration of 2.8 x 10^12 m^-3 are moving due north at a speed of 2.0x10^6 m/s. Also, a 7.0 x 10^11m^-3 concentration of (O2)- (dioxygen -)ions is moving due south at a speed of 7.2 x 10^6m/s. Determine the...
  10. S

    Mapping unit circle from one complex plane to another

    I want to show that if the complex variables ζ and z and related via the relation z = (2/ζ) + ζ then the unit circle mod(ζ) = 1 in the ζ plane maps to an ellipse in the z-plane. Then if I write z as x + iy, what is the equation for this ellipse in terms of x and y? Any help would be...
  11. A

    What is the Frequency Content of a Unit Step Signal in Fourier Analysis?

    how a step function has frequency content in it? thanks
  12. S

    Inverse Laplace transform with unit step function

    Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...
  13. R

    Fuel per unit distance decreasing?

    I was reading a link i found here on physicsforums called "The relativistic rocket". There was lots of calculations of the required fuel for certain distances and such. However, I understand that time→0 when our velocity v→c. And that will mean we travel a larger distance for a shorter...
  14. D

    Work on unit vector notation for matrices?

    I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!
  15. H

    MHB Why do you divide the components by the magnitude when finding a unit vector?

    Say for example v = <3,4> I was taught to divide each component by the magnitude in order to get the unit vector, i.e. 3^2 + 4^2 = ||v||^2 5 = ||v|| So the unit vector of that vector is <3/5,4/5> or 1/5<3,4> But if I forgot that I had to divide the components by the magnitude, I would not...
  16. C

    MHB Minimum area of an odd number-sided, equilateral polygon with side lengths of 1 unit.

    Suppose you look at all of the equilateral (non-self-intersecting) polygons** with an odd number of sides, and each side length is equal to 1 unit. For examples, the polygon with the fewest number of sides in this group is the equilateral triangle, and then the next one is an equilateral...
  17. Z

    Context Free Grammar (eliminate the unit of production rules)

    I have grammar S → ABaC | BaC | AaC | ABa | aC | Aa | Ba | a A → B | C | BC B → b C → D D → d Can someone please help me to eliminate all the rules of grammar production unit. Thanks for help! :biggrin:
  18. G

    Need help with half-life of C-14 question (exponents unit)

    Question: Carbon-14 has a half-life of 5730 years. A bone is found in which \frac{7}{8} of the original [16g of] carbon-14 has decayed. How old is the bone? Formula: C(t)=Co(\frac{1}{2})\frac{t}{H} (it's hard to see but it says \frac{1}{2} to the power of \frac{t}{H}) C(t) - the number at...
  19. P

    Conductance per unit length of a co-axial cable (Intro to Electromagnetics)

    Homework Statement Starting with: G = \frac{I}{V}= \frac{-\int_{s}\sigma\mathbf{E}\cdot d\boldsymbol{s}}{-\int_{l}\boldsymbol{E}\cdot d\boldsymbol{l}} Derive the conductance per unit length, G', of a coaxial cable by assuming a line charge of \rho_{l} on the center conductor...
  20. S

    What does the unit hp means?

    What does the unit "hp" means? I admit that my physics sucks because it has been a long time since I heard the word "physics" but putting that aside, what does the unit "hp" represent/means? I don't remember learning that unit in school. Eg. An engine develops 85hp I'm guessing it's a Power...
  21. B

    Should the Astronomical Unit be replaced by the Light Second/Light Minute Etc.?

    Now that other solar systems have been discovered, as well as binary and trinary star systems, is the helio-geocentric Astronomical Unit still useful? Wouldn't it be clearer to use the terms light second, light minute. light day, light year, etc., instead? Obviously, these terms are still...
  22. S

    Should luminous intensity be a fundamental unit?

    It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.
  23. T

    Relavtivity Question - Unit Needed

    1. The problem I need to know what unit I would use for my calculated velocity? 2. Relevant Information T (Relative Time) = 9 years To (Stationary Time) = 2 years U (Velocity) = ? Solution? What unit would I use for the velocity received?
  24. D

    How Do You Calculate Per Unit Values for a 20MVA Motor at 13.8kV?

    1) I'm not sure how to solve this question A 20MVA induction motor connected at 13.8kV draws a load current of 1.0 p.u, 0.85 power factor lag. Calculate the rated load current in Amps and the real power and reactive power drawn by the motor. Express these quantities in per unit form using...
  25. C

    Prove Cone over Unit Circle Homeomorphic to Closed Unit Disc

    Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...
  26. R

    Finding the unit normal of a vector field

    I'm on the last chapter of a 1200 page calc book, I'm really psyched. Homework Statement The Attempt at a Solution The method I learned for finding the unit normal of a vector field, n, is take the derivative of the equation and divide that by the magnitude of the...
  27. Steve Zissou

    Unit of Measure of Exponentiated Item

    Hello. Let's say we have the quantity f=1/(1+x) where x has no unit of measure. What is the unit of measure of f, once we take f^t, where t can be in years? Thanks
  28. K

    Force per unit length between two parallel whires of +/- X volts

    Homework Statement Two parallel whires, separated by a distance D (midpoint distance), are charged with a current density L (each whire has a radius R). If the whires have the potential +/- X Volts, what is the force per unit length between them? Homework Equations B = μ0*I /(2πr) is...
  29. Z

    Show that function maps unit cirle onto a line

    Homework Statement Show that the function f(z) = z/(1-z) maps the unit circle to an infinite line. Homework Equations Polar form z = rexp(iθ) The Attempt at a Solution I've tried to see what happens, when we let f(z) = f(eiθ) and then get: f(eiθ) = eiθ/(1-eiθ) But I need some...
  30. M

    What are Chords? What is the smallest unit in physics?

    What are Chords? What is the smallest "unit" in physics? Someone told me they read a Yahoo AP article stating the most basic "building block" of the universe was a sound wave, and upon discovery this had been named a chord(or perhaps cord/kord/etc). Again, this was an AP article, but I...
  31. A

    Unit vectors and vector quantities (notation)

    When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it...
  32. P

    Representing Force as a Unit Vector - Explained

    Our teacher taught us a way to represent a force as a unit vector. Suppose a force of 12 N acts along the line 2i+j-2k. The force is written as: F = 12 N (2i+j-2k/√1^2+2^2+2^2) Therefore, F = 8i+4j-8k But, I can't understand why is it so. Please explain.
  33. I

    Unit Conversion: Astronomical Units, Parsecs and Light Years

    Hi everyone, It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem: Question "The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is...
  34. J

    How is 100 W produced over 24 hours in Edexcel Unit 4 Specimen Paper?

    Homework Statement Please can someone look at the attached question (I have extracted MS and relevant previous pieces of information) Where do they get the idea that 100 W is produced over 24 hours ?? Homework Equations The Attempt at a SolutionI know power = work done / time but if power...
  35. H

    Trouble with the unit normal vector for stokes theorem

    We're given x^2+2*y^2=1. so x^2=1-2y^2 now using distance formula d^2=x^2+y^2 since x^2=1-2y^2, substituting it in the distance formula we get: d^2=1-2y^2+y^2=1-y^2; differentiating and then setting the eq to 0 we get; 0=-4y or y=0. now x^2=1-2y^2=1 so x=+-1 so point having...
  36. Z

    Simple Atomic Mass Unit question

    Homework Statement The uranium isotope 235U captures a neutron and undergoes fission to produce 93Rb and 141Cs. Calculate the energy released in this process. The nuclear masses of the relevant isotopes are 235U 235.0439u, 93Rb 92.9217u, 141Cs 140.9195u Homework Equations...
  37. E

    Find Value of q for Unit Vector PQ: Homework Equation Solution

    Homework Statement Given vector OP = 2i+3j, OQ = qi+2qj. How can i find the possible value for q? note that PQ is a unit vector. Homework Equations Given (p-1)i + (2p-6)j having magnitude 10, find p The Attempt at a Solution From the formula, i was told that the unit vector...
  38. D

    MHB Proof: Let $f$ be a Nonconstant Entire Function on the Unit Disc

    Let $f$ be a nonconstant entire function that maps the unit circle, $\{z: |z| = 1\}$, into itself. Prove that $f$ maps the open unit disc, $\{z: |z| < 1\}$, into itself. I am having a little trouble starting this one. z in C
  39. I

    Holomorphic function on the unit disc

    Does there exist a holomorphic function f(z) on the unit disc and satisfies f(1/n) = f(-1/n) = 1/n^3 for every n in N?
  40. D

    MHB Finding the Zeros of $1+z^{2^n}$ on the Unit Disc

    Why doesn't $1+z^{2^n}$ have zeros on the unit disc?
  41. Y

    Understanding Hydraulic Resistance: A Comparison to Electrotechnics

    For better understanding of it's principles, electrotechnics is often compared to hydronics (and, probably, vice versa). But, why having the electrical resistance to a flow of charged particles - with it's basic unit "Ohm", there in general Physics is no unit of measurement of the hydronic...
  42. D

    Is Every Point on the Unit Circle an Accumulation Point of Zeros for f(z)?

    Let f(z) = \prod\limits_{n = 1}^{\infty}(1 - nz^n) Prove that each point on the unit circle is an accumulation point of zeros of f So we have that z = \sqrt[n]{1/n} . Now where do I go from here? Probably should note that this is a Weierstrass Product.
  43. D

    Energy, work, power unit 3 question

    Homework Statement The diagram provided shows a man pulling a box across the floor. Assume that the force of the friction can be ignored and that the acceleration of the box is 1.27 m/s. Find the angle to the horizontal that the man must pull. 65N figure located on the rope the person is...
  44. S

    Calculating Cost Per Unit of Solar Energy from Data Sheet

    Homework Statement I don't know if this is a physics problem per se but its from physics class. So we were supposed to pick out a solar panel and figure out what is the cost per unit of energy for this form of solar energy? I know where supposed to use the data sheet for the panel that we...
  45. C

    Unit tangent vectors, Normal vectors, and Gradients

    So I'm kinda new to Physics Forums but I've been using threads as guides for about a year now. Basically, I'm hardcore studying for my Calc III exam (the final is in a few weeks) and I came across an interesting lapse in my understanding (well many in fact, but one in particular). First of...
  46. M

    HELP Mass per unit length equation

    Homework Statement Ok so using the standard equation v = Sqrt(T/Mu) I want to find Mu as a gradient for the first fundamental. I've made it into F x lambda = sqrt(T/Mu) Then f x 2l = sqrt(T/Mu) Then f= sqrt(T/4l^2 Mu) As I'm having the tension held by a mass suspended over a pulley. f=...
  47. C

    MHB Solving for Unit Vectors in U Given Vector 1 and Matrix S

    So I am given the vector 1...but I need to find vector 2 and 3, in order to find U=(v1, v2, v3), and U is a unitary matrix. Vector 1 is: (1/2+1/2i 1/2 1/2i)^T The example from my notes shows me how to find U, but I am also given a matrix S to start with... Any clue where to start?
  48. J

    Electric field - multiple choice - Physics Unit 4 Specimen

    Homework Statement see attached file Homework Equations The Attempt at a Solution ok so I get that the answer is B but is it because they have the same q/m ratio?
  49. T

    Vector Calculus, Unit normal to surface help

    Homework Statement If \phi(x,y,z) = x3 + 2xy +yz3 find \nabla\phi at the point P=(1,1,2) and direction of the unit normal to the surface \phi(x,y,z) = 11 at P. Homework Equations The Attempt at a Solution Worked out \nabla\phi to be 5i + 10j + 12k Got |\nabla\phi|= √256 so the...
  50. J

    Unit vector cross products in different co-ords

    hey, i've been trying to work out how to determine the sign of cross products of unit vectors, for example in cylindrical, r x z = - theta theta x z = r r x theta = z i can't figure out the sign, r x z = |r||z|sinβ theta where β is the angle between them, which is 90°...
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