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. M

    Show Uniform Continuity Help

    [PLAIN]http://img258.imageshack.us/img258/78/52649134.jpg So I've thought of a few ideas on how to prove this, but only one so far that I've sort of figured out what to do. What I want to do is split the interval up in two, so from [0,b] and from (b, ∞), for some b in the reals. Now since f is...
  2. R

    Radius of the path of an accelerating object in uniform Circular motion

    Homework Statement A 2 kg car travels in a flat circle. At a certain instant the velocity of the car is 24 m/s West and the total acceleration of the car is 9 m/s 2 at 53 degrees North of West. What is its radius? Answer in units of km. Homework Equations F=ma w=(2pi)/T a= w^2...
  3. S

    Uniform Convergence of Continuous Functions: A Proof?

    Homework Statement As in the question - Suppose that f_n:[0,1] -> Reals is a sequence of continuous functions tending pointwise to 0. Must there be an interval on which f_n -> 0 uniformly? I have considered using the Weierstrass approximation theorem here, which states that we can find...
  4. Demon117

    Uniform convergence of piecewise continuous functions

    I like thinking of practical examples of things that I learn in my analysis course. I have been thinking about functions fn:[0,1] --->R. What is an example of a sequence of piecewise functions fn, that converge uniformly to a function f, which is not piecewise continuous? I've thought of...
  5. V

    Pointwise and uniform convergence of fn(x) = (1-x)^(1/n)

    Homework Statement Let fn(x) = (1-x)^(1/n) be defined for x an element of [0,1). Does the sequence {fn} converge pointwise? Does it converge uniformly? Homework Equations The formal definition of pointwise convergence: Let D be a subset of R and let {fn} be a sequence of real valued...
  6. P

    PDF of the sum of three continous uniform random variables

    Homework Statement X1, X2, X3 are three random variable with uniform distribution at [0 1]. Solve the PDF of Z=X1+X2+X3. Homework Equations The Attempt at a Solution PDF of Z, f_z=\int\intf_x1(z-x2-x3)*f_x2*f_x3 dx2 dx3 I saw the answer at http://eom.springer.de/U/u095240.htm, but I cannot...
  7. M

    Conservation of momentum and a uniform rod

    Homework Statement The uniform rod (length 0.60 m, mass 1.0 kg) in Fig. 11-54 rotates in the plane of the figure about an axis through one end, with a rotational inertia of 0.12 kg·m2. As the rod swings through its lowest position, it collides with a 0.20 kg putty wad that sticks to the end of...
  8. I

    Uniform circular motion Lab

    In a lab we were supposed to produce a rollercoaster ramp while it had a loop, and then to drop a marble at a height where it would finish the entire path without falling off, with enough centripetal acceleration at the loop. we were not given the mass of the marble, and we were only given a...
  9. T

    Uniform Continuty in the plane R2

    Homework Statement Hello, I'm having trouble understanding the best way of attacking some uniform continuity questions, in two variables. The questions state a subset A of R2 on which to study this: 1) f(x,y) = (x/1+x^2)+(y/1+y^2), A=R2 2) f(x,y) = sin^2(x^2+y^2-1)/cos(x^2+y^2-1)...
  10. B

    Finding Momentum with Uniform Magnetic Field: q, B, a, d

    Homework Statement A particle of charge q enters a region of uniform magnetic field B (pointing into the page). The field deflects a particle a distance d above the original line of flight. Is the charge positive or negative? In terms of a, d, B, and q, find the momentum of the particle. x...
  11. D

    Two functions f/g Uniform Continuity

    I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous? I have a feeling it is not but I can't seem to find a counter example.
  12. M

    Non Uniform Circular Motion Problem

    A new car is tested on a 200m diameter track. If the car speeds up at a steady 1.5 m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangental acceleration? So we know that our acceleration is equal to 1.5 m/s^2, our radius of our circle is 100m. I...
  13. W

    Uniform Circular Motion Space Station question

    Homework Statement A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), as shown in the figure (http://session.masteringphysics.com/problemAsset/1057181/4/GIANCOLI.ch05.p048.jpg). The circle formed by the tube has a radius of...
  14. J

    Rotational Energy, 2 blocks and a pulley (solid uniform sphere)

    Homework Statement Consider the system below. The mp = 20.0 kg 'pulley' is a solid uniform sphere of radius of 0.250 m with the frictionless axle passing through its diameter. The mass of the block on the incline is m1 = 16.0 kg , and the coefficient of kinetic friction between the two...
  15. M

    Uniform distribution on the disc

    Homework Statement consider a disc of radius 1 in the plane D in R^2 D = {(x,y) in R^2 | x^2 + y^2 <=1 } what is the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint distribution of xy is 1/Pi for x^2 + y^2 <=1 right? but how exactly? "density"...
  16. M

    Uniform distribution of a disc

    Homework Statement Consider a disc of radius 1 in the plane D in R D = {(x,y) in R | x^2+y^2 <= 1} write the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint pdf is 1/Pi for x^2 + y^2 <= 1 <- correct? but how to I get the marginal pdfs?
  17. R

    Uniform Distribution Expected Value

    Homework Statement If X~(-5,5) find E[||X|-2|] Homework Equations If a variable is distributed uniformly then f(x) = 1 / (b-a), with a mean of (a+b)/2. If x~u, then y~u. The Attempt at a Solution I think I should change the variable, so y = |X| - 2, and then find E[|y|]. So if I...
  18. L

    Uniform distribution of a disc

    1. Homework Statement Here is the link to the old thread, https://www.physicsforums.com/showthread.php?t=349730 i tried posting but it doesn't seem active. I don't understand how they get the second pdf as i tried it and got the first pdf. I also don't know how to do the double integral as...
  19. Y

    Single circular loop of wire filled with a uniform magnetic

    Homework Statement The figure to the right shows a single circular loop of wire filled with a uniform magnetic field pointing into the page The radius of the loop is R = 1.75 cm. The magnitude of the magnetic field in the loop is changing according to B(t) = B0 exp{-t / 2.15sec} (a) what is the...
  20. P

    Will an Airplane Maintain Uniform Circular Motion While Banking?

    Homework Statement General question:Decide wether an airplane will continue to fly in uniform circular motion while banking on a turn. Homework Equations m(v2/r) \SigmaFx= Lsin\theta=m(v2/r) \SigmaFy=Lcos\theta-mg=0 The Attempt at a Solution my question is if the centripetal force...
  21. N

    Uniform Continuity: Proof of Limit Existence

    Homework Statement Assume f:(0,1) \rightarrow \mathbb{R} is uniformly continuous. Show that \lim_{x \to 0^+}f(x) exists.Homework Equations Basic theorems from analysis.The Attempt at a Solution The statement is intuitive but I'm having trouble formalizing the idea. Uniform Continuity means...
  22. A

    Conservation of Angular Momentum of uniform disk

    Homework Statement A uniform disk turns at 8.6 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk, see the figure. They then turn together around the spindle with their centers...
  23. J

    Uniform Continuity in Bounded Functions and Limits: Examples and Proofs"

    Homework Statement a) Give an example of a bounded continuous function f: R -> R which is not uniformly continuous. b) State (in terms of a small Epsilon and a large K) what it means to say that f(x) -> 0 as x -> infinity (plus or minus) c) Now assume that f: R -> R is continuous and...
  24. I

    Center of mass of a uniform density square centered at the origin. Offset by width/4?

    Homework Statement To get used to finding the center of mass of an object, I have decided to start with a uniform density square. The square is centered at the origin. The center of mass should be at the center of the square, and thus at the origin. When I tried to solve this however, my...
  25. D

    Finding the angle in a Uniform Circular Motion problem?

    1. Alright say you have a simple pendulum with given mass, length, and velocity (I think.. correct me if I'm wrong) ... how would I go about calculating theta (in degrees)? 2. I'm assuming the quadratic eq will have to be used? Among a couple of the simple force formulas. 3. I...
  26. B

    Uniform Continuity on Closed and Bounded Intervals

    Homework Statement Suppose that f: [0, \infty) \rightarrow \mathbb{R} is continuous and that there is an L \in \mathbb{R} such that f(x) \rightarrow L as x \rightarrow \infty. Prove that f is uniformly continuous on [0,\infty). 2. Relevant theorems If f:I \rightarrow \mathbb{R} is...
  27. J

    What Determines the Velocity of a Falling Chain?

    Homework Statement uploaded Homework Equations rocket equation The Attempt at a Solution i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.
  28. P

    Will I Slide in My Seat During a 2km Level Turn at 400km/hr in an Airplane?

    Homework Statement you are sitting in an airplane. you have a window seat. the plane makes a level turn of 2km at speed 400km/hr. the coefficient of static friction btwn you and the seat is .35 Then they ask is the frictional force sufficient to keep you moving in a radius of 1km at a speed...
  29. N

    MATLAB code to Generate Uniform Random Variable

    Homework Statement Generate 1,00,000 triplets(sets of three) of Uniform random variables on [0,1]. Y be max of each triple and Z be min of each triple. Derive the densities for these RV from theory and compare histograms of Y and Z with densities found in theory. Homework Equations...
  30. A

    Simple 2-D Uniform Motion Problem

    A ball rolling with an initial velocity of 40 m/s [W] undergoes an acceleration of 5.0 m/s^2 [N] for a period of 6.0 seconds. a) What is the final velocity of the ball? b) What is the displacement of the ball in the 6.0 seconds? Can someone explain how I would draw this vector...
  31. S

    Uniform circular motion - stone in pail

    Homework Statement A stone rests in a pail that is moved in a vertical circle of radius 60 cm. What is the least speed the stone must have as it rounds the top of the circle if it is to remain in contact with the pail? Answer: 2.4 m/s Homework Equations v= 2 pi r / t The Attempt at...
  32. S

    Uniform circular motion mass problem

    Homework Statement A mass of 1.5 kg moves in a circle of radius 25 cm at 2 rev/s. Calcualte (a) the tangential velocity, (b) the acceleration, (c) the required centripetal force for the motion. Answers: A) 3.14 m/s B) 39.4 m/s^2 radially inward C) 59 N Homework Equations v=2piR/T...
  33. L

    Nonconducting surface uniform charge hole

    Homework Statement Didn't know what to put for thread title, my notes and textbook were a little to ambiguous A large, flat, nonconducting surface carries a uniform charge density σ. Into the middle of this sheet has been cut a small, circular hole of radius R. Ignoring fringing fields from...
  34. C

    Electrostatic self energy of a uniform density sphere

    Homework Statement "In class we calculated the electrostatic self energy of a uniform density sphere of charge, i.e., the work required to assemble the sphere from "infinite dispersal." Along the same lines, calculate the electrostatic self energy of a spherical shell of charge, of negligible...
  35. radou

    Determining whether Rω is connected in uniform topology

    Homework Statement As the title suggests. Rω is the space of all infinite sequences of real numbers. The uniform topology is induced by the uniform metric, which is, on Rω, given with: d(x, y) = sup{min{|xi - yi|, 1} : i is a positive integer} The Attempt at a Solution I am trying to show...
  36. H

    Static Friction and Uniform Circular Motion

    Homework Statement A cat sits on a merry go round at a radius of 4.0m from the center. The ride makes one complete rotation every 6.3 seconds. What is the least coefficient of static friction to keep the cat in place? Homework Equations Circumference = 2Pi*r V=d/t a=v^2/r The...
  37. M

    Uniform circular motion of a particle

    Homework Statement A particle's position is given by the formula r(t) = Rcos(ωt)î + Rsin(ωt)ĵ The particle's motion at t=0 can be described as a circle starting at time t=0 on the positive x axis. a) When does the particle first cross the negative x axis? b) Find the speed of the particle at...
  38. C

    Calculating Distance Traveled with Uniform Acceleration

    Homework Statement A ball starts from rest and rolls down a hill with uniform acceleration, traveling 180 m during the second 4.4 s of its motion. Homework Equations The Attempt at a Solution How far did it roll during the first 4.4 s of motion?
  39. A

    Uniform magnetic field problem

    A proton (mass= 1.7×10-27 kg, charge= 1.6×10-19 C) traveling with speed 106 m/s enters a region of space containing a uniform magnetic field of 1.2 T. What is the time t required for the proton to re-emerge into the field-free region? I plugged the numbers into r=mv/qB and then t=pi r/ v...
  40. A

    Uniform solid sphere rolling on inclined plane

    Homework Statement A uniform solid sphere,rolls without slipping on a horizontal surface with an angular velocity \omega,meets a rough inclined plane of incination 60(degrees).The sphere starts pure rolling up the plane with an angular velocity.Find the new angular velocity . Homework...
  41. T

    Solving for Net Torque on Uniform Mass Density Rod

    Homework Statement A rod has a uniform mass density of 0.05 kg/cm it has a moment of inertia equal to 0.1ML^2. The rod sweeps out an area equal to 0.25* pi meters squared in 4 seconds. If you apply a net torque of -1/16 Nm to the rotating rod, how many revolutions will the rod make before...
  42. L

    Force on a charge from a line of uniform charge density

    Homework Statement Write an equation in vector component form for the force when a point charge q0 is located a distance d from a vertical rod of uniform charge density Q and length L on the 45o line that bisects the positive x and y axes. basically if you can picture a rod going vertically...
  43. G

    Uniform electric field moving a proton and electron

    Homework Statement A uniform electric field of magnitude 640 N/C exists between two parallel plates that are 4.00 cm apart. A proton is released from the positive plate at the same instand that an electron is released from the negative plate. Determine the distance from the positive plate that...
  44. J

    How do you put a uniform charge on an insulator?

    To put a uniform charge on the surface of a conducting hollow sphere one just needs to touch it at one point with an electrode. To put a uniform charge on the surface of an insulating hollow sphere, do you have to somehow physically spray charge all over it?
  45. radou

    Continuity of a mapping in the uniform topology

    Homework Statement Let (a1, a2, ...) and (b1, b2, ...) be sequences of real numbers, where ai > 0, for every i. Let the map h : Rω --> Rω be defined with h((x1, x2, ...)) = (a1x1 + b1, a2x2 + b2, ...). One needs to investigate under what conditions on the numbers ai and bi h is continuous...
  46. C

    Light reflected by uniform glass sphere

    Homework Statement S solid uniform glass sphere is surrounded by air. The sphere has radius R and refractive index n. As shown in the picture, a light ray traveling in air, parallel to a diameter of the sphere, enters the sphere, reflects off the far side, then exits the sphere traveling in a...
  47. C

    Uniform distribution on simplex

    How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?
  48. U

    Uniform Circular Motion of a car

    Homework Statement If a curve with a radius of 60 meters is properly banked for a car traveling 60 km/hr, what must the coefficient of friction be for a car on the same curve traveling 90 km/hr? Homework Equations Fmax = u * Fn where Fmax = force causing the friction, u = coefficient of...
  49. U

    Uniform Circular Motion of dice

    Homework Statement Fuzzy dice hang from the rear-view mirror of a car rounding a curve. If the curve has a radius of 275 meters and the dice are hanging at an angle of 12° from the vertical, how fast is the car going? Homework Equations a = v2/R for an acceleration with a constant...
  50. C

    Uniform distribution on high dimensional space

    I would like to ask how to define a uniform distribution on a high dimensional spaceR^n. What is the density of such distribution?
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