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. A

    Linear Velocity vs Uniform Velocity

    I was hoping someone could help clarify. Does uniformly increasing velocity also mean linearly increasing velocity? I found terms where it used uniform exponential. So I'm confused as to whether the word "uniform" used alone would also refer to a linear change.
  2. W

    Calculating the Inertia Tensor of cone with uniform density

    Homework Statement Calculate the moments of inertia I_1, I_2, and I_3 for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the x_3 axis along the axis of symmetry of the cone. Choose the origin at the apex of the cone, and calculate the elements of the...
  3. I

    Hydrostatics - Benzene poured into uniform U shaped tube with water

    Homework Statement A uniform glass tube is bent into a U shape. Water is poured into the tube till it stands 10cm in each tube. Benzene (sp gr = 0.879) is then slowly added to the tube on the left side until the water rises 4cm on the right. What length is the column of benzene when the...
  4. PhysicoRaj

    Electrostatic force in a medium of non uniform permittivity

    Homework Statement Two point charges, +4 μC and -10 μC are placed 10 cm apart in air. A dielectric slab of large area and thickness 5 cm is placed between the charges. Find the force of attraction between the charges, if the dielectric has a dielectric constant of 9. Homework Equations...
  5. paulmdrdo1

    MHB Speed of sound - Uniform motion- linear equation application

    I need help with these problems. 1. Speed of Sound in Air. Two seconds after firing a rifle at a target, the shooter hears the impact of the bullet. Sound travels at 1100 feet per second and the bullet at 1865 feet per second. Determine the distance to the target (to the nearest foot). 2...
  6. I

    Finding velocity of particles in a uniform magnetic field

    Homework Statement Given are a uniform electric field, E = 30,000 V/m inside a capacitor (see picture), and a uniform magnetic filed, B = 10 T, perpendicular to the plane of the page, present in all of the area. Identical charged particles are moving in a trajectory marked by the dashed...
  7. N

    Why do all points on a uniform disc have the same angular velocity?

    ω = dΘ/dt if any points on a uniform disc have the same angular velocity then the corollary implies that any point on the disc must transverse 2π rad in the same amount of time. Is there a mathematical way to demostrate this or is this only demostratable purely by experiement?
  8. T

    PDF of arccos and arcsin of a uniform random number

    Homework Statement I want to find the PDF for arccos and arcsin of a uniform random number. Given: Y\sim\mathcal{U}(0,2\pi) \\ X = cos(Y) The Attempt at a Solution I started with trying to find the CDF: \begin{align} F_X& = P(X \le x) \\ & = P(cos(Y) \le x) \\ & = P(Y \le arccos(x))...
  9. B

    Uniform Convergence of a Sequence of Functions

    Homework Statement Define f_n : \mathbb{R} \rightarrow \mathbb{R} by f_n(x) = \left( x^2 + \dfrac{1}{n} \right)^{\frac{1}{2}} Show that f_n(x) \rightarrow |x| converges uniformly on compact subsets of \mathbb{R} Show that the convergence is uniform in all of \mathbb{R}...
  10. A

    Uniform Circular Motion and Centripetal Force

    Hey guys, first post here! Hoping to get a little help. Homework Statement You are a traffic safety engineer in charge of determining safe speeds for roads. A particular banked curve has a radius of 11.0 meters and is banked at an angle of 8.00°. The coefficient of static friction between...
  11. F

    Matlab continuous uniform distribution

    Homework Statement Generate 100 data points from a continuous uniform distribution with mean = 10 and variance = 4 Homework Equations u = (a+b)/2 var = (b-a)^2 / 12 r = a + (b-a).*rand(100,1); The Attempt at a Solution points = 100 m1 = 10 v1 = 4 syms a b [a...
  12. S

    Uniform magnetic field and electric field

    Homework Statement How would you find the period of a charged particle in an uniform electric and magnetic field? The charged particle has velocity that is perpendicular to the magnetic and electric field (which are directed in the x-axis). Homework Equations F=q(E+vxB) The Attempt...
  13. T

    Electric field of a non uniform charge of a cylinder

    Homework Statement A very long solid cylinder of radius R = 4.2 cm has a non-uniform volume charge density along its radial dimension, given by the function ρ = Ar2, where A = +2.2 µC/m5. a)How much total charge is contained on a 1 m length of this cylinder? b)Outside: What is the...
  14. P

    Uniform circular motion and angular momentum?

    Homework Statement A sphere on top of a table is attached to a rope which goes through a hole in the table and is attached to a bucket at the other end. The sphere moves in a uniform circular motion with radius R. Water is then added to the bucket and the radius for the sphere's circular...
  15. S

    Proof uniform convergence -> continuity: Why use hyperhyperreals?

    A uniformly convergent sequence of continuous functions converges to a continuous function. I have no problem with the conventional proof. However, in Henle&Kleinberg's Infinitesimal Calculus, p. 123 (Dover edition), they give a nonstandard proof, and they use the hyperhyperreals to do it. I...
  16. Duderonimous

    Gaussian sphere problem, non uniform charge

    Homework Statement A solid non conducting sphere of radius R=5.60 cm has a nonuniform charge ditribution ρ=(14.1 pC/m^3)r/R, where r is the radial distance from the spheres center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r=0, (c) r=R/2.00...
  17. Q

    MHB Deriving Y-Component of Uniform Electric Rod | E=-▽V

    This is essentially the problem. And this is what I did. Realizing the following: E = -▽V I simply took the derivative in regards to the vertical component, in this case "a". So: -dV/da [the above formulae] And I got the following: Κλl/(a sqrt(l^2+a^2)) Does that seem about right...
  18. L

    Range of uniform convergence for a series

    Homework Statement Find the range of uniform convergence for the following series η(x) = ∑(-1)n-1/nx ζ(x) = ∑1/nx with n ranging from n=1 to n=∞ for both Homework Equations To be honest I'm stumped with where to begin altogether. In my text, I'm given the criteria for uniform...
  19. G

    Compute voltage inside sphere of uniform charge

    Homework Statement Problem 2.21 from Introduction to Electrodynamics, David J. Griffiths, Third Edition. Find the potential inside and outside a uniformly charged solid sphere who's radius is R and whose total charge is q. Use infinity as your reference point. Homework Equations...
  20. C

    Three charges q, uniform circular motion

    Homework Statement Two spheres have a charge of q a stationary sphere between them has a charge of -q. The 2 positive spheres move like conical pendulums at a constant velocity of 12.0m/s in uniform circular motion. What is the magnitude of charge q? Homework Equations Electric Force...
  21. S

    MHB Pointwise convergence implies uniform convergence

    Hi, I have to prove the following theorem: Let $f_n:[0,1] \to \mathbb{R}, \forall n \geq 1$ and suppose that $\{f_n|n \in \mathbb{N}\}$ is equicontinuous. If $f_n \to f$ pointwise then $f_n \to f$ uniformly. Before I start the proof I'll put the definitions here: $f_n \to f$ pointwise if and...
  22. L

    Conducting bar in a uniform magnetic field

    I'm studying for the MCAT and this problem came up. The correct answer is D. However the explanation was very confusing. The explanation is verbatim: " Let's start by considering A. Using the right-hand rule on a current running through the wire in figure 2 shows you that the rod is pushed...
  23. A

    Uniform continuity and the sup norm

    Suppose I have a function f(x) \in C_0^\infty(\mathbb R), the real-valued, infinitely differentiable functions with compact support. Here are a few questions: (1) The function f is trivially uniformly continuous on its support, but is it necessarily uniformly continuous on \mathbb R? (2) I...
  24. U

    Electric field of a point charge in uniform motion

    In Griffiths Chapter 12, pg 527: Suppose a point charge is moving along x, we obtain the following E-fields: Questions 1. Is the vector R solely in the x-y plane? 2. What happened to the coordinate 'z' ? 3. Why are they only doing things in the 2-D plane? Can we use rotational...
  25. S

    Uniform distribution Probability

    John is going to eat at at McDonald's. The time of his arrival is uniformly distributed between 6PM and 7PM and it takes him 15 minutes to eat. Mary is also going to eat at McDonald's. The time of her arrival is uniformly distributed between 6:30PM and 7:15PM and it takes her 25 minutes to eat...
  26. D

    Parametric hypothesis, uniform distribution

    Homework Statement We are given a sample of size 100. After some tests (histogram, Kolmogorov) we deduce the sample X is distributed uniformly. The next task is to presume the parameters are equal to values of your choice, and test if such hypothesis is true. Homework Equations The Attempt at...
  27. P

    Sum of two independent uniform random variables

    Hi, http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf (see page 8, sum of two independent random variables). I don't understand why they had to go further into the limits, 1 < z < 2. Why do they have to do that? And also, where did they get it...
  28. S

    Time dilation and uniform circular motion

    Hi, I've taken a course in SR and studied GR on my own, but I do not know how to solve problems of this type. This is just purely for fun, not homework related at all. A particle of mass m is moving on a circle of radius R at constant linear velocity v = .8c. If the particle makes N...
  29. P

    Statistics Problem - Uniform Distribution

    Hi, The question is: http://puu.sh/5GX2G.jpg http://puu.sh/5GX2G.jpg I am not exactly sure what the question is asking. Here is the answer/solution: http://puu.sh/5GX68.png But I am not sure what is going on. Could someone please explain what exactly the question is asking...
  30. AakashPandita

    Proof of no net gravitational force on a particle inside uniform shell

    In my book it is written that Newton's shell theorem can be used to show that a uniform shell of matter exerts no net gravitational force on a particle located inside it. How?
  31. S

    Propagating waves along a non uniform string.

    Homework Statement The linear mass density of a non uniform wire under constant tension decreases gradually along the wire so that the incedent wave is transmitted without reflection. the wire is uniform for* -∞≤x≤0 In this region, a transverse wave has the form y(x,t) = 0.003cos(30x − 60t)...
  32. Ascendant78

    Gravity and uniform circular motion involving a loop?

    Homework Statement A 0.27 kg toy car is held at rest against a 1796 N/m spring compressed a distance of 8cm. When released, the car travels a distance of 112cm along a flat surface before reaching a 0.30m high loop. The friction coefficient of the flat surface and the toy car is (0.4...
  33. R

    Stresses in triangular plate with one edge under uniform loading

    Homework Statement A 45° triangular plate ABC built in at BC and loaded by a uniform pressure p0 on the upper edge AB. The inclined edge AC is traction free. Find the stresses in the plate. Homework Equations Stress function: \phi =...
  34. C

    Random process of uniform- graphing and pdf

    Homework Statement Word for word of the problem: Let N (t, a) = At be a random process and A is the uniform continuous distribution (0, 3). (i) Sketch N(t, 1) and N(t, 2) as sample functions of t. (ii) Find the PDF of N(2, a) = 2A. Homework Equations A pdf is 1/3 for x in...
  35. H

    The magnetic field of a spinning spherical shell of uniform charge

    In chapter 5, magnetostatics, of Griffiths' Introduction to Electrodynamics (third edition), there's a problem in the back of the chapter that asks you to calculate the force of attraction between the northern and southern hemispheres of a spinning charged spherical shell. The problem in its...
  36. P

    Free Charge Moving in Uniform Magnetic Field

    Homework Statement The drawing shows a particle carrying a positive charge +q at the origin (of x and y axis), as well as a target location located in the lower left quadrant. The target is just as far from the x-axis as it is from the y axis. There is also a uniform magnetic field...
  37. R

    Uniform circular motion and tension of a string

    Homework Statement a 0.60 kg sphere rotates around a vertical shaft supported by 2 strings, as shown. if the tension in upper string is 18N calculate. a) tension in lower string? b) rotation rate (in rev/min) of the system. Homework Equations The Attempt at a Solution...
  38. T

    Convergence in Uniform and L2 sense, function interpretation

    Let: gn(x) = 1 in [1/4 - 1/n2 to 1/4 + 1/ n2) for n = odd 1 in [3/4-1/n2 to 3/4 + 1/n2) for n = even 0 elsewhere Show the function converges in the L2 sense but not pointwise. My issue is in how I should use the definition of...
  39. T

    Proving Non-Uniform Convergence: Understanding the Role of Singular Points

    I have a question where I am supposed to show that a series does not converge uniformly, I get the majority of the question, but one part in the solution I can't see the rationale or how they decided on the result: It has to do with the partial sum: SN= (1 - (-x2)N+1)/ (1+x2) The...
  40. M

    Electric field due to uniform charged line

    Homework Statement Find the electric field at point p 5cm away from a 10cm line with a uniform charge of 2x10^-4C. so its uniformly charged from 0 - 10cm and then point p is at 15cm This question is broken down into 4 step by step parts: first is to consider 100 individual...
  41. Philosophaie

    Spherical Ball with uniform Charge Density

    I want to find ##\Phi## and ##\vec{E}## for the general case of a Spherical Ball with uniform Charge Density centered at the origin radius d. ##\Phi = \frac{\rho}{4*\pi*\epsilon_0}\int\int\int\frac{r^2*sin\theta}{|r-r'|}dr d\theta d\phi## ##E =...
  42. D

    Proof That The Following System Does Uniform Oscilations

    Homework Statement Well, we are given the following system, in which the rope, spring, and pulley is ideal. We know that for the angle a the system is in equilibrium. The question is, to show that if the angle a is small, the system does unfirom oscilations. I don't know how to tackle this...
  43. L

    Uniform Convergence Homework: Is ##f_n(x) = \frac{x}{1+nx^2}##?

    Homework Statement Is the sequence of function ##f_1, f_2,f_3,\ldots## on ##[0,1]## uniformly convergent if ##f_n(x) = \frac{x}{1+nx^2}##? 2. The attempt at a solution I got the following but I think I did it wrong. For ##f_n(x) = \frac{x}{1+nx^2}##, I got if ##f_n \to0## then we must...
  44. L

    Uniform Convergence of ##\{f_n\}## on ##[0,a]##

    Homework Statement Show that the sequence of functions ##x,x^2, ... ## converges uniformly on ##[0,a]## for any ##a\in(0,1)##, but not on ##[0,1]##.2. The attempt at a solution Is this correct? Should I add more detail? Thanks for your help! Let ##\{f_n\} = \{x^n\}##, and suppose ##f^n \to...
  45. ShayanJ

    Center of mass of a uniform sphere

    We know,by symmetry,that the center of mass of a uniform sphere is at its center.So we expect the formula r_{com}=\frac{\int r \rho d\tau}{\int \rho d\tau} to give us zero for this case.So let's see: r_{com}=\frac{\int_0^{R} \int_0^{\pi}\int_0^{2\pi} r^3 \sin{\theta} d\phi d\theta...
  46. phosgene

    Uniform convergence of sequence of functions

    Homework Statement Let f_{n}(x)=\frac{x}{1+x^n} for x \in [0,∞) and n \in N. Find the pointwise limit f of this sequence on the given interval and show that (f_{n}) does not uniformly converge to f on the given interval. Homework Equations The Attempt at a Solution I found that the pointwise...
  47. L

    Is x^2 Not Uniformly Continuous on the Real Numbers?

    Homework Statement Show that the function ##x^2## is not uniformly continuous on ##\mathbb{R}## Homework Equations Delta - Epsilon Definition: ##\exists \epsilon > 0, \ \forall \delta >0, \exists x \in S [|x-x_0|< \delta \text{and} |x^2 - x_0^2| \ge \epsilon ].## The Attempt at a...
  48. E

    Uniform convergence of a product of functions

    Homework Statement Let \left[a,b\right] be a closed bounded interval, f : [a,b] \rightarrow \textbf{R} be bounded, and let g : [a,b] \rightarrow \textbf{R} be continuous with g\left(a\right)=g\left(b\right)=0. Let f_{n} be a uniformly bounded sequence of functions on \left[a,b\right]. Prove...
  49. R

    MHB Applied Stochastic processes: difference of uniform distributions

    Two independent random variables X and Y has the same uniform distributions in the range [-1..1]. Find the distribution function of Z=X-Y, its mean and variance. =Using change of variables technique seems to be easiest. fX(x) = 1/2 fY(y) =1/2 f = 1/4 ( -1<X<1 , -1<Y<1) Using u =x -y...
  50. Q

    Uniform Circular Motion: Solving for String Tension

    Homework Statement A ball of mass 4 kg on a string of length 1.5 m is being swung in a circle in the vertical plane at a constant speed of 10 m/s. Find the tension in the string at the bottom and top of the balls path Homework Equations ƩF = m(v^2/r) The Attempt at a Solution This is how I...
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