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

    Uniform continuity of functions like x^2

    Why some functions that are continuous on each closed interval of real line fails to be uniformly continuous on real line. For example x2. Give conceptual reasons.
  2. G

    The inverse of uniform random variable

    Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...
  3. A

    Show that f Uniform Differentiable implies f' Uniform Continuous

    Homework Statement A function f:(a,b)\to R is said to be uniformly differentiable iff f is differentiable on (a,b) and for each \epsilon > 0, there is a \delta > 0 such that 0 < |x - y| < \delta and x,y \in (a,b) imply that \left|\frac{f(x) - f(y)}{x - y}-f'(x)\right| < \epsilon. Prove that...
  4. M

    Find gravitational potential inside uniform ball

    Homework Statement Find the potential and force on a mass m outside and inside the Earth in terms of g, the acceleration due to gravity, assuming Earth has uniform density and radius R.Homework Equations For a mass m, the potential energy of it in the gravitational field of a spherical shell of...
  5. U

    Uniform Lateral Pressure on a bar.

    Hey all, been struggling through this question all afternoon, was wondering if someone could shine some light on the subject please? QUESTION: If a uniform lateral pressure of 80MN/m (2), is applied to the four sides of the bar, in addition to the axial load, find the contraction on the...
  6. T

    Numerical Analysis: Uniform Continuity Question

    This isn't so much of a homework problem as a general question that will help me with my homework. I am supposed to prove that a given function is uniformly continuous on an open interval (a,b). Since for any continuous function on a closed interval is uniformly continuous, I am curious...
  7. M

    Probability of X being greater than Y for independent uniform variables

    Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M
  8. H

    Uniform Convergence of nx/nx+1

    I am given f_n(x)=\frac{nx}{nx+1} defined on [0,\infty) and I have that the function converges pointwise to 0 \ \mbox{if x=0 and} 1\ \mbox{otherwise} Is the function uniform convergent on [0,1] ? No. If we take x=1/n then Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5...
  9. Z

    Uniform Convergence of Fourier Series

    Homework Statement Find the minimum number required (value of n) for the average deviation of the Fourier Series to fall below 2% Homework Equations Use the Uniform Convergence of Fourier Series. Where Sm is the partial sum of the Fourier Series. C is constant. Here C is ∏^2 So...
  10. S

    Uniform circle motion question

    Homework Statement A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of...
  11. A

    Physical pendulum made of a uniform disk

    Homework Statement A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum? Homework Equations The Attempt at a Solution
  12. M

    Uniform circular motion question

    Please look at the picture... It is of a blue object in four locations that is swung around with a rope ( red line ) in a circle with constant velocity... I wanted to know if my diagrams are correct for each separate location... and I was hoping someone could check my work below to tell me...
  13. A

    How can I solve for the mass and radius in this uniform circular motion problem?

    Homework Statement A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.01 m/s in a horizontal circle, as illustrated in the figure. If the angle the string makes with the vertical is 38°, and the tension of the string...
  14. M

    Two real analysis problems: proving constancy and a uniform convergence problem

    The problem statement Let f:[a,b]→\mathbb{R} be differentiable and assume that f(a)=0 and \left|f'(x)\right|\leq A\left|f(x)\right|, x\in [a,b]. Show that f(x)=0,x\in [a,b]. The attempt at a solution It was hinted at that the solution was partly as follows. Let a \leq x_0 \leq b. For all x\in...
  15. 1

    Integral Formulas for Center of Mass of Uniform Density

    Homework Statement I'm being given problems regarding the center of mass of a uniformly dense object, and I am told by the textbook to use: \frac{1}{V}\int x dV I have no idea what to do with that. I'm pretty sure I won't be learning anything about multiple variable integrals for two...
  16. N

    Uniform Circular motion problem,

    1. At a distance of 25km from the eye of a hurricane, the wind is moving at 180km/h in a circle. What is the magnitude of the centripetal acceleration, in meters per second squared, of the particles that make up the wind? Homework Equations Ac=V^2/r = 4∏^2r/T^2 = 4∏^2rf^2 The Attempt...
  17. A

    Calculating Speed of Rotating Disks and Hoops Using Uniform Solid Disk Equations

    Homework Statement A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle. (a) What is the speed of its center of mass when...
  18. V

    Bending of light in a uniform gravitational field

    Homework Statement This is supposed to be a simple problem that shows that light bends or gets pulled in a gravitational field. A light pulse emitted in the positive x direction travels 10 s in a uniform gravitational field of 100 m/s^2. the gravitational field points in the negative y...
  19. C

    Uniform Circular Motion/Newton's 2nd Law?

    Homework Statement Question: A 3.45 kg object is attached to a vertical rod by two strings as in Figure P6.11. The object rotates in a horizontal circle at constant speed 5.65 m/s. What are the tensions of the two strings, individually? Variables: m = 3.45kg length of both strings...
  20. A

    Uniform Acceleration-Algebraically

    b]1. Homework Statement [/b] An object was displaced 19.6 m east while uniformly accelerating from rest. If the average velocity of the object was 5.00 m/s east, what was the rate of acceleration? Homework Equations The Attempt at a Solution So my Vo=0 Vf= 5.00m/s east x=19.6m...
  21. J

    Uniform ladder sliding on smooth surface

    Homework Statement A uniform ladder of length L and mass M has one end on a smooth horizontal floor and teh other end against a smooth vertical wall. The ladder is initially at rest in a vertical plane perpendicular to the wall and makes an angle \theta0 with the horizontal. (a) Write down the...
  22. S

    Acceleration in Uniform Circular Motion

    Homework Statement What is the acceleration (in m/s^2) of a 10 kg mass moving with speed 2 m/s in uniform circular motion about a circle of radius 2m? Homework Equations F=ma a=v^2/r in uniform circular motion The Attempt at a Solution Seems simple enough. To find the...
  23. W

    How to verify a uniform distribution on n-sphere

    suppose we have many dots on a unit n-sphere i suspect that they satisfy the uniform distribution but how to verify this?
  24. S

    Uniform acceleration of moving wagon

    Homework Statement A child pushes his friend in a wagon along a horizontal road and then let's go. The wagon rolls for 10.0 seconds before stopping. It travels a distance of 20.0cm during the last 1.00s of its motion. Assuming uniform acceleration, (a) How fast was the wagon traveling at the...
  25. A

    How far does the car travel? Uniform acceleration.

    Homework Statement A car accelerates uniformly from rest to a speed of 23.2 km/h in 5.4s. Find the distance it travels during this time. Answer in units of m. Homework Equations \Deltax = 1/2(vi + vf)t vf = vi + at vf2 = vi2 + 1/2 at2 The Attempt at a Solution I have used...
  26. A

    Simple bug on uniform rod rotational momentum problem

    Homework Statement A small 10.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 60.0g and is 90cm in length...
  27. P

    Poisson Distribution/ uniform dist.

    I am in an error analysis class and our homework has asked us this (we will be writing a computer program to do this): "Create a sample with 396 draws from a Poisson distribution with N=1000 and 4 draws from the uniform distribution between 0 and 105. This sample represents data from a CCD...
  28. W

    Simple Uniform Acceleration Question

    Homework Statement Hello new user here. I'm utterly confused about uniform acceleration as my book does a very poor job (in my opinion) of explaining it. Could somebody please help me with this problem? A spaceship far from any star or planet experiences uniform acceleration from 65.0m/s to...
  29. A

    Non uniform circular motion

    Homework Statement car travels in a flat circle of radius r. at certain point instantaeous velocity is 24 m/s west and the total acceleration is 2.5 m/s2 53 degrees north of west. find radial and tangential acceleration. and periodHomework Equations ar= 2.5cos37 at=2.5sin37 r=24 x 24/ar T=...
  30. A

    Perturbation of a uniform electrostatic field by a dielectric cube

    Hi, Is there any way to analytically calculate the perturbation of a uniform electrostatic field by a dielectric cube. I know a solution exists for dielectric spheres but I haven't been able to come across the solution, when dealing with a cube. Ohh.. and I'm assuming the simplest case...
  31. T

    Uniform distribution transform: e^2x

    X is a uniformly distributed random variable on a [-1, 1] range. (i.e. X is U(-1, 1)) Find the distribution of e^2X: I feel like it has something to do with the uniform's relation to exponential function, but i get stuck. I begin by using inverse transform: Fy(y) = Fx[ln(y)/2] fy(y)...
  32. T

    Uniform acceleration kinematics lab

    Homework Statement This is more of a general question but it is part of my physics course so i decided to post here, I am sure many of you have done this lab but what it is is a cart with tickertape attached to it going down a ramp, once we plot a d-t graph there are lots of application...
  33. N

    Is \frac{1}{\sqrt{x}} uniformly continuous in (0,1)?

    i need to prove that \frac{1}{\sqrt{x}} is not uniformly continues in (0,1) for epsilon=0.5 |\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}|=|]\frac{\sqrt{y}-\sqrt{x}}{\sqrt{xy}}\frac{\sqrt{y}+\sqrt{x}}{\sqrt {y}+\sqrt{x}}|=|\frac{y-x}{(\sqrt{y}-\sqrt{x})\sqrt{xy}}|...
  34. DocZaius

    Frequency of oscillating electric dipole in uniform field without using diff eq

    Homework Statement Electric dipole makes small angle with uniform electric field. Find the frequency of the oscillation using dipole moment p, moment of inertia I, and field magnitude E. Homework Equations Torque=I*(angular acceleration)=I*(theta)'' Torque=p*E*sin(theta) The...
  35. Barnak

    Uniform distribution on a toroidal surface

    I'm not sure this is the right thread to post my problem : I'm trying to define a uniform distribution on the toroidal surface associated to a dipolar magnetic field (or electric). More specifically, the surface (in 3D euclidian space) is parametrised as this, using the usual polar...
  36. F

    Electron traveling parallel to a Uniform Electric Field

    Homework Statement An electron with speed 2.0E7 m/s is traveling parallel to a uniform electric field of magnitude 1.18E4 N/C. How far will the electron travel before it stops? How much time will elapse before it returns to its starting point q = 1.60E-19 C mass of electron = 9.11E-31...
  37. P

    How is tangential accleration zero in uniform circular motion?

    How is tangential accleration zero in uniform circular motion?? Homework Statement the magnitude of tangential velocity is same but the directions are different..so how can the tangential acceleration be zero?? Homework Equations The Attempt at a Solution
  38. R

    Total mass of a cord, uniform density

    Homework Statement http://i54.tinypic.com/2uztu6d.jpg Homework Equations I don't know how to use LaTeX, sorry... mass = L times integral of density, where the endpoints are the bounds of the region. However, in this case...it seems to me that things are reserved... The Attempt at...
  39. K

    Cauchy Sequence of Continuous Fns: Uniform Convergence?

    Is it true that a cauchy sequence of continuous functions defined on the whole real line converges uniformly to a continuous function? I thought this was only true for functions defined on a compact subset of the real line. Am I wrong?
  40. N

    Uniform electrical field - why?

    In a uniform electrical field, why does the field strength remain constant? For a field where two metal plates, one negatively charged the other positively charged, why will E, electric field strength, always remain constant? If we assume the distance between two plates A & B, where A has a...
  41. B

    Dynamics of uniform circular motion

    A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. The sensor measures the magnitude of the normal force that the seat exerts on a rider. The loop-the-loop ride is in the vertical plane and its radius is 21 m...
  42. B

    Uniform circular motion, trapeze artists problem

    Lewis is a trapeze artist. He is hanging upside down on a swing bar; he is holding on to the swing bar with his knees. Lewis is holding his partner Amanda below him, who weighs 475 Newtons. Assume that Amanda moves on a circle that has a radius of 6.50 meters. At a swinging speed of 4.00 m/s...
  43. B

    Uniform circular motion, earth's rotation

    The Earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the Earth is a sphere with a radius of 6.38 x 106 m, determine the speed and centripetal acceleration of a person situated at a latitude of...
  44. L

    Torque experienced by a current loop in uniform magnetic field

    Homework Statement Revered members, please see my attachment (1) In this diagram, PQRS is a rectangular current loop and I is the current and its direction is shown in red arrow . B is the magnetic field and it acts from left to right and n is the normal drawn to the plane of the loop...
  45. R

    Non Uniform Circular Motion w/ Calculus and Vectors

    Hello! I have a problem which is solvable using simpler methods, but I'm trying to use it as a bridge to understanding how to do these problems in a more rigorous setting. Homework Statement A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/hr to 50 km/hr in the...
  46. B

    What would the universe be like if c were not uniform

    I sort of understand Einstein's theory of relativity. I'm trying to visualize what the universe would be like if the speed of light were added on to moving objects. objects are moving in so many directions that it's hard to understand how one would even add the speed of light on to a motion...
  47. R

    Proving a Uniform Energy Distribution of B in Decay A -> B + C

    Homework Statement Consider the decay A -> B + C (where A is not at rest). In the rest frame of A, B is emitted in a random direction (all directions have equal probability) and I need to show that in the lab frame, the energy distribution of B is uniform. (We assume that B has negligible...
  48. D

    Real Analysis: Continuity and Uniform Continuity

    Question: Show that f(x)= (x^2)/((x^2)+1) is continuous on [0,infinity). Is it uniformly continuous? My attempt: So I know that continuity is defined as "given any Epsilon, and for all x contained in A, there exists delta >0 such that if y is contained in A and abs(y-x)<delta, then...
  49. G

    Induced emf when accelerates in uniform magnetic field

    Hi everyone, This question is bothering me for days and would hope to receive some help in this forum. This question is with regards to Faraday's law on EMI. Will an emf be induced when a copper rod is accelerated between a uniform magnetic field? My answer would be no if the rod has...
  50. B

    Uniform continuity and Bounded Derivative

    Hi, All: Let f R-->R be differentiable. If |f'(x)|<M< oo, then f is uniformly continuous, e.g., by the MVTheorem. Is this conditions necessary too, i.e., if f:R-->R is differentiable and uniformly continuous, does it follow that |f'(x)|<M<oo ? Thanks.
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