What is Uniform: Definition and 1000 Discussions

A uniform is a type of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform.

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  1. S

    Find Equilibrium: Solving a Uniform Bar Problem

    Homework Statement A uniform bar AB of length l and weight W is hinged to the wall at its end A and supported by means of a string of length a which is tied to the wall as shown. Find the angle \theta that the bar will make with the wall corresponding to the position of equilibrium...
  2. J

    Uniform circular motion merry-go-round

    Homework Statement A purse at radius 1.90 m and a wallet at radius 2.60 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2) + (4.60 m/s2). At that instant and in...
  3. M

    Economics and uniform series formula problems

    Homework Statement A Machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for $3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the...
  4. N

    Uniform Circular Motion: Understanding the Characteristics and Misconceptions

    Homework Statement Which, if any, of the following statements about a particle in uniform circular motion is/are true? Its acceleration vector is a constant. Its velocity and acceleration vectors are always perpendicular. The direction of its acceleration is toward the center of...
  5. D

    Electric field over a non uniform surface charge

    Homework Statement A non-uniform surface charge lies in the xz-plane. At the origin, the surface charge density is (sigma)=3.01C/m^2; other charges are present in the vicinity as well. Just to the right of the origin the y-component of the electric field is 520,000N/C. What is the y-component...
  6. D

    Energy of a Dipole in a Uniform E Field

    Homework Statement The graph shows the potential energy of an electric dipole which is in a constant electric field; only the electric force is acting on the dipole. Consider a dipole that oscillates between +/- 51 degrees. What is the dipole's kinetic energy when it is aligned with the...
  7. M

    Uniform Charge Distribution. Find total charge.

    Homework Statement We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box? Homework Equations The Attempt at a Solution I have an...
  8. A

    Analysis of Person Diving into Pool w/ Uniform Horizontal Beam

    Homework Statement An 80kg person is preparing to dive into a pool. The diving board is a uniform horizontal beam that is hinged to the ground at point A and supported by a frictionless roller at D. B is the point directly under the center of gravity of the person. The distance between A to B...
  9. E

    Show Uniform Convergence of fn to f in Compact Metric Space

    Homework Statement Alright, here is the problem. Given a compact metric space X, and a sequence of functions fn which are continuous and f_{n}:X->R (reals), also f_n->f (where f is an arbitrary function f:X->R). Also, given any convergent sequence in X x_{n}->x, f_{n}(x_{n})->f(x). The problem...
  10. N

    Uniform convergence of series

    Homework Statement Does the following series converge uniformly? [sum from n=1 to inf] \frac{e^{-nx}}{n^2} on [0, inf) Homework Equations I know I need to use the M test or Cauchys Principle of uniform convergence. My tutor suggests using the former if there is uniform convergence...
  11. B

    Impulse given to 7 cm uniform thin stick. Translation and rotation happen

    Homework Statement A uniform thin rod 7.0 cm long with a mass of 40.0 g lies on frictionless horizontal table. It is struck with horizontal impulse at right-angle to its length, at a point 2.0 cm from one end. If the impulse is 8.5 mN*s: describe the resulting motion of the stick...
  12. M

    Motion of charged particle in uniform magnetic field

    Homework Statement Accelerating voltage of 2500V is applied to an electron gun producing a beam of e- originally traveling horizontally north in a vacuum toward a viewing screen 25cm away. a. What are the magnitude and direction of the deflection caused by Earth's gravitational field? b. What...
  13. G

    Expected value of the log of a uniform distribution

    Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1
  14. A

    Uniform acceleration: air track, data error?

    Homework Statement [edit]: In case anyone didn't get a clear picture, in a nutshell the experiment involves us releasing a glider down an air track within a fixed distance x, where the time, t taken is then recorded down. Sorry for not mentioning this before if it's of any use. To determine...
  15. S

    MLE, Uniform Distribution, missing data

    I would like to determine the MLE for k in U(0,k) where U is the uniform pdf constant on the interval [0,k] and zero elsewhere. I would like this estimate in the case of missing data. To be specific, what is the MLE for k given the three draws X={1,3,*} where * is unknown.
  16. C

    Electrostatic Potential from a uniform line of charge?

    Homework Statement a) What is the value of an electrostatic potential V, a distance r from a point charge Q? b) A uniform line of charge, of linear charge density (\lambda), extends along the x-axis from x = 0, to x = a. i) By considering the contributions from the infitisimal elements...
  17. F

    Pointwise vs. uniform convergence

    A function is pointwise bounded on a set E if for every x\in E there is a finite-valued function \phi such that |f_n(x)|<\phi(x) for n=1,2,.... A function is uniformly bounded on E if there is a number M such that |f_n(x)|<M for all x\in E, n=1,2,.... I understand that in uniform...
  18. J

    Uniform Continuity: Polynomial of Degree 1 - What is \delta?

    hi everyone I was reading one example about Uniform continuity, say that the polynomials, of degree less than or equal that 1 are Uniform continuity, my question is, for example in the case polynomial of degree equal to one Which is \delta, that the Uniform continuity condition satisfies...
  19. W

    Uniform convergence of a series

    Homework Statement We know that f is uniformly continuous. For each n in N, we define fn(x)=f(x+1/n) (for all x in R). Show that fn converges uniformly to f. Homework Equations http://en.wikipedia.org/wiki/Uniform_convergenceThe Attempt at a Solution I know that as n approaches infinity...
  20. B

    <p> and <p^2> for uniform psi

    <p> and <p^2> for uniform "psi" Homework Statement What is <p> and <p^2> for state: \begin{array}{l} \psi (x) = {\rm{constant for x}} \in {\rm{[ - a,a]}} \\ \psi (x) = {\rm{0 for x}} \notin {\rm{[ - a,a]}} \\ \end{array} ...that is: a "psi" that is constant within...
  21. T

    A Charged Particle in a Uniform Electric Field

    Hi. I'm curious, how would a charged particle, let's say an electron, move in a simple uniform electric field? My first guess would be that it would follow Newton's second law of motion and move with a constant acceleration: $ \dot{x}=\frac{Eq}{m} $ where E is the fields intensity, q the...
  22. S

    Calculating Sound Power from Intensity and Distance

    Homework Statement A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source? Just a simple answer check to see if my answer is reasonable. Homework Equations \beta = 10 db log (I/I0)...
  23. C

    Uniform Circular Motion - python program

    Hello guys. I am taking an introductory course in computer programming. For one assignment I was to make up a word problem, then write a program to solve it. I wrote a program to calculate the radius of a circular orbit based on the orbiting object's current velocity, and other parameters. Can...
  24. A

    Linear acceleration in a uniform magnetic field due to torque

    Here the extra credit question I'm stuck on: A square loop (perimeter of 4L and hinged along one side) is made of a wire that has a mass per unit length of 0.1000 kg/m and carries a current of 5.000 A. A uniform magnetic field of 10.00 mT directed perpendicular to the hinged side exists in...
  25. estro

    Uniform convergence - Series of functions

    Homework Statement \mbox{Check whether } \sum_{n=0}^\infty \frac {1}{e^{|x-n|}} \mbox{ is uniform convergent where its normaly convergent} The Attempt at a Solution \mbox{I choose } \epsilon = 1/2 a_n=\frac {1}{e^{|x-n|}}\ ,\ b_n= \frac {1}{n^2} \lim_{n\rightarrow\infty} \frac {a_n}{b_n}=0\...
  26. F

    Uniform circular motion statements

    Homework Statement Which of the following is not true in relation to an object moving in uniform circular motion? a. KE of the object is constant b. net force is zero c. net work is zero d. the magnitude of acceleration is constant e. momentum is non-constant The Attempt at a...
  27. estro

    Proving Uniform Convergence of f_n(x) in [a,b]

    Homework Statement Suppose: f(x)\ and\ f'(x)\ are\ continuous\ for\ all\ x \in R For\ all\ x \in R\ and\ for\ all\ n \in N\ f_n(x)=n[f(x+\frac{1}{n})-f(x)] Prove\ that\ when\ a,b\ are\ arbitrary,\ f_n(x)\ is\ uniform\ convergent\ in\ [a,b] The Attempt at a Solution\lim_{n\rightarrow...
  28. S

    Dipole moment of sphere with uniform volume charge Q

    Homework Statement Determine the dipole moment, \mathbf{p}, of a sphere of radius R with a uniform volume charge, total Q, with respect to its center. Homework Equations \mathbf{p}=\int \mathbf{r} \rho(\mathbf{r}) d\tauThe Attempt at a Solution I know that \mathbf{p}=\mathbf{0}, but I have a...
  29. S

    Acceleration of particles with differing masses in a uniform electric field

    Homework Statement The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates. If the plates are moved closer together A X and Y will both remain...
  30. M

    Can all subsequences of a function sequence in C([0,1], R) converge uniformly?

    Let y_n be a sequence of functions in \mathcal{C}([0,1], \mathbb{R}) Suppose that every subsequence of y_n has a subsequence that converges uniformly. Prove that they all converge to the same limit.
  31. R

    Uniform convergence and continuity

    1.kn (x) = 0 for x ≤ n x − n, x ≥ n, Is kn(x) uniformly convergent on R? I can show that it is uniformly convergent on any closed bounded interval [a,b], but I don't think it is on R. Could anyone please give me some hints how to prove it? 2.Fix 0 < η < 1. Suppose now...
  32. E

    Uniform circular motion; two balls, two cables, and a post; no gravity

    Homework Statement In space in the absence of gravity, there is a post of "infinite mass," meaning that the post is fixed or "nailed down" and cannot move. A ball of mass m1 is connected to the post by a cable of negligible mass of length L1. A second ball of mass m2 is connected to the first...
  33. N

    How uniform is the expansion of the universe?

    The universe is known to be expanding. There is no centre of expanision, since it's space itself that is expanding, rather than galaxies speeding away from us through space. But if the expansion is uniform, wouldn't the space between molecules expand as well as the space between galaxies? If...
  34. V

    Non uniform charge distribution on conductor surface

    Hey everyone! I need some help. Can a non uniform charge distribution exist on a conductor's surface due to some external influence? Please explain bearing in mind that a conductor's surface is equipotential.
  35. R

    Uniform Continuity Homework: Show h is Uniformly Continuous on [0, ∞)

    Homework Statement Show that if h is continuous on [0, ∞) and uniformly continuous on [a, ∞), for some positive constant a, then h is uniformly continuous on [0, ∞). Homework Equations The Attempt at a Solution I'm thinking of using the epsilon-delta definition of continuity...
  36. R

    Finding Angular Acceleration of Uniform Rod

    Homework Statement A uniform rod of length 0.750 m and mass 1.20 kg is pivoted at one end by a smooth pin as shown below. The rod is released from the vertical position and given a slight nudge to release it from the vertical position of unstable equilibrium...
  37. D

    Calculating required pump pressure to maintain flowrate in a uniform horizontal pipe

    Homework Statement I am having trouble with calculating the required pump pressure in a horizontal water pipe, 3Km long. i know that the flowrate is 600Kg/s, average velocity 5.6m/s, cross-sectional area of pipe is 0.107143m^2 and losses due to friction average 0.002 per meter Homework...
  38. M

    Electron Uniform Field Question

    Hi, I have a problem working out the answer to one part of a type of uniform field question. My answers to the first three parts of the question are correct, but I'll write out those parts as well because I think it's necessary, to understand the second part: An X-ray tube is operated at 25...
  39. I

    Uniform Distribution, Absolute Value

    Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...
  40. C

    Electrons in rectilinear uniform motion

    Im wondering if electrons in rectilinear uniform motion will 'feel' an external magnetic field...?
  41. B

    Uniform continuity in top. spaces

    So my teacher said that uniform continuity was a metric space notion, not a topological space one. At first it seemed obvious, since there is no "distance" function in general topological spaces. But then I remembered that you can generalize point-wise continuity in general topologies, so why...
  42. L

    Uniform convergence problem

    let f is a continuous, real-valued function on [a,b] then, for any e, there exist a polygonal function p such that sup|f(x)-p(x)|<e using uniform convergence, this might be shown... but i cannot figure it out...
  43. E

    Finding PDF of uniform distribution

    Homework Statement Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y? Homework Equations fX(x) = 1/ lambda . exp (-x/...
  44. E

    MATLAB for uniform random variables

    Homework Statement Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g = (x,y) = sqrt (-2ln(x) . cos(2piy). Since finding the distribution of g(X,Y) analytically is quite tough, I need to generate MATLAB program for 1 - 10,000...
  45. R

    (Easy?) Probability Q: Uniform in Uniform

    Hello I have been struggling with a simple probability question. Homework Statement We are given that X is a uniformly distributed random variable on [0, 1]. After X is chosen, we take another uniform [0, 1] random variable Y (independent of X) and choose the subinterval that Y falls in. L...
  46. C

    Using Dirichlet's test for uniform convergence

    Homework Statement Show that \sum(-1)^(n+1) / (n + x^2) converges uniformly but not absolutely on R. Homework Equations Using Dirichlet's Test for uniform convergence. (fn) and (gn) are sequences of functions on D satisfying: \sum fn has uniformly bounded partial sums gn -> 0...
  47. L

    Sum of two continuous uniform random variables.

    Z = X + Y Where X and Y are continuous random variables defined on [0,1] with a continuous uniform distribution. I know we define the density of Z, fz as the convolution of fx and fy but I have no idea why to evaluate the convolution integral, we consider the intervals [0,z] and [1,z-1]...
  48. estro

    Uniform continuity of composite function

    I'll be very thankful is someone will tell me where I'm wrong. We know: 1) f is uniform continuous. 2) g is uniform continuous. We want to prove: fg(x) is uniform continuous. proof: from 1 we know -> for every |a-b|<d_0 exists |f(a)-f(b)|<e from 2 we know -> for every |x-y|<d...
  49. B

    Pointwise Limits and Uniform Convergence Help

    Hi all Came across this question which i have attempted to answer but am sure i have gone wrong somewhere, any help would be appreciated... Suppose fn(x):R-->R, where fn(x)=x+(1/n) (n belongs to N). Find the pointwise limits of the sequences (fn), (1/n fn) and (fn2). In each case determine...
  50. S

    Uniform Circular motion problem

    Uniform Circular motion problem! Homework Statement A 235 m tall tower is built on the equator. Due to the rotation of the earth, how much faster does a point at the top of the tower move than a point at the bottom (in m/s)? Homework Equations v=w*r (w is omega) The...
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