Uniform Definition and 1000 Threads

Hi all, I'm trying to generate uniform random vectors with n dimensions. To be more precise, each of the elements of the vector must be a uniform distributed variable in [0,1] The constraint is that the sum of the elements of the vector must be 1. I tried different solutions for over a week but...

Homework Statement Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force...

It sounds like an easy-enough problem, but even writing down the ridiculously nonlinear equation that would need to be solved is making my face hurt. I'm talking classical/Newtonian gravitation, action-at-a-distance, constant-force. It could really be any external non-EM conserved force...

Hi guys, I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent? Thank you

Homework Statement I have a physics final coming up and instead of problems, the final will cover multiple choice conceptual questions. "Several identical charged particles, each with charge Q and mass M, move in a region of uniform magnetic field B. The only force any of the particles...

I don't understand uniform continuity :( I don't understand what uniform continuity means precisely. I mean by definition it seems that in uniform continuity once they give me an epsilon, I could always find a good delta that it works for any point in the interval, but I don't understand the...

Homework Statement A 1380 N uniform boom of length ℓ is supported by a cable, as shown. The boom is pivoted at the bottom, the cable is attached a distance 3/4ℓ from the pivot, and a 3604N weight hangs from the boom’s top. Find the tension of the cable. here is a picture of the diagram...

Homework Statement (X,d1),(Y,d2) and (Z,d3) are metric spaces, Y is compact, g(y) is a continuous function that maps Y->Z with a continuous inverse If f(x) is a function that maps X->Y, and h(x) maps X->Z such that h(x)=g(f(x)) Show that if h is uniformly continuous, f is uniformly...

Homework Statement A straight uniform stick of L= 1m and mass m = 1 KG lies on a surface of a frozen lake.Someone kicks the stick at one end,imparting an impulse of 2Ns normal to the stick.Describe the subsequent motion of the stick. Homework Equations I=mΔV The Attempt at a...

Homework Statement A solid, insulating sphere of radius a has a uniform charge density of ρ and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c, as shown. A). Find the magnitude of the electric field in the...

Homework Statement A uniform electric field between two parallel plates has magnitude of 20N/C and is directed downward. 1) A charge brought into this field experiences a force of 10.0 N downward. The charge must be...? 2) The potential energy of this charge when moving downward...

I'm really struggling to get my head around some of the mechanics applications in my calculus module and would really appreciate it if somebody could help me get my head around it. I have this question: A particle P of constant mass m has a position vector: r=x(t)i+y(t)j, and moves...

Hi guys, New here, i have a question which has been doing my head in for days now. Hope someone might know how to answer it. The question is: A car travels with uniform acceleration from rest and is observed to cover distances of 6m and 7.5m respectively in two consecutive intervals of 1...

Homework Statement d\hat{S}/dt = γ\hat{S} \times \hat{B} What is the physical interpretation of this equation i.e. what is the behavior of the magnetic moment in an uniform magnetic field?Homework Equations I don't think I need any equation for this, just intuition or vector calculus identity...

Homework Statement Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension. (A & B) I did (C,D, E) I need help (a) What variables are being measured / manipulated in this lab? What type of relationship is being...

For example the microcanonical ensemble uses a dirac delta distribution on a certain energy shell E, which is not actually a uniform distribution (even on the energy shell), but it comes close. Why is uniformity (in phase space, or a relevant restriction thereof) natural for equilibrium...

Homework Statement A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field, as shown in the figure below. When E = (A + B) N/C, where A and B are positive numbers, the ball is in equilibrium at the angle θ. (a) Find the charge on the ball...

An object moves in the xy-plane in a uniform circular motion. We know that there is two forces action upon the object. One we have that is F1, F2 is unknown. Both vectors speed : 4m/s radius : 4m mass : 1kg F1 : 10 i N (i as in x-direction vector) F2 : ? (bound to be in the xy-plane)How do I...

A ball of mass m is attached by two strings to a vertical rod. as shown above. The entire system rotates at constant angular velocity about the axis of the rod. a)Assuming ω is large enough to keep both strings taut, find the force each string exerts on the ball in terms of ω, m, g, R, and ...

I am trying to make a game where a drone approaches a ship, that may be moving, and then orbits it at a set distance. I know that if the drone is already moving in a circle of uniform motion then I use a = \frac{v^{r}}{r} I then take that magnitude and an angle derived from atan2 with cos...

See attachment. I don't why a charged particle in a uniform magnetic field will move in a circle. Why can't it just continue straight in the direction its going until another force acts on it?

Homework Statement A spot of paint on a bicycle tire moves in a circular path of radius .33m. When the spot has traveled a linear distance of 1.66m, through what angle has the tire rotated? Homework Equations v=rw w=2∏/T The Attempt at a Solution 1.66=2∏/T 1.66T=2∏ 100∏/83

Homework Statement Prove that if F is uniformaly continuous on a bounded subset of ℝ, then F is bounded on A. Homework Equations The Attempt at a Solution F is uniformaly continuous on a bounded subset on A in ℝ. Therefore each ε>0, there exists δ(ε)>0 st. if x, u is in A where...

A fishing boat leaves port at 04:30 h in search of the day's catch. The boat travels 4.50km[E], then 2.50km[S], and finally 1.50km[W] before discovering a large school of fish on the sonar screen at 06:30h. a) What is the boat's average speed. b) Calculate the boat's average velocity.Solved a)...

Homework Statement The second hand on a watch has a length of 4.5mm and makes one revolution in 60s. What is the speed of the end of the second hand as it moves in uniform circular motion? Homework Equations ac=v^2/r The Attempt at a Solution ac=v^2/4.5

If the function f:D→ℝ is uniformly continuous and a is any number, show that the function a*f:D→ℝ also is uniformly continuous. Ok, so I am just learning my proofs so be patient with me, I'm very new at it. take a>0, ε>0 and x,y in D. We know |x-y|<δ whenever |f(x)-f(y)|<ε. If we take...

Homework Statement f(x)= {1, ‐1/2<x≤1/2} {0, ‐1<x≤ ‐1/2 or 1/2<x≤1} State whether or not the function's Fourier sine and cosine series(for the corresponding half interval) converges uniformly on the entire real line ‐∞<x<∞ Homework Equations The Attempt at a Solution...

Hi Physics Forumites I have tried to find a post which I didn't bookmark - foolish me. It discussed uniform accelerated motion in relativistic terms and, unusually, incorporated initial velocities, all in very nice LaTeX. I have scanned a bunch of threads on rocket motion, but can't find it...

Homework Statement A non uniform rod of length L=1m and linear mass density: λ(x)=λo(1-(x/2L)) with λo=1Kg/m. It is supported at it's midpoint and initially tips over so that it's left end lies on the ground. Part a: Find the position of the centre of mass along the rod when it is in it's...

Homework Statement Homework Equations The Attempt at a Solution I understand that all i need to do is plug these two points into the formula and subtract to get the correct area, but i am not provided a mean or variance as i normally am, so I'm at a loss.

Homework Statement A normally functioning clock has a radius of 30cm. What is the average acceleration in the first 15 seconds if the second hand starts at 12? What is the instantaneous acceleration when the second hand is at 12? Homework Equations v = d/t a = Δv / Δt limit as Δt...

Homework Statement A bridge takes 2 minutes to open up fully from 0 to 80 degrees. The first 20 degrees it is accelerating, and the last 60 degrees it is traveling with even velocity. I will have to find acceleration for the first 20 degrees and angular velocity for the last 60 degrees...

Homework Statement Let f be continuous on the interval [0,1] to ℝ and such that f(0) = f(1). Prove that there exists a point c in [0,1/2] such that f(c) = f(c+1/2). Conclude there are, at any time, antipodal points on the Earth's equator that have the same temperature. Homework Equations...

I need these Questions answers in 2 hours! :p Any help would be greatly appreciated. Homework Statement Question 3 Mathematically derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions. Question 4 Use your results...

Anyone know how the theory of Uniform Circular Motion was discovered? I know Newton invented the word "centripetus", Latin for Centripetal but that's about it. I can find history on the pendulum but nothing for uniform circular motion. Could you give me some names? Or links to some...

Homework Statement A long wire carrying 100 A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero? Homework Equations B = iμo/2∏R The Attempt at a Solution I...

Hello, I'm currently in high school and going over discrete uniform distribution, and we've come across this formula. I'm curious if anyone could show me how the formula is true, as when I asked my teacher he just said that it'll confuse the class and we don't need to know why it's true. If...

Hey everyone. I haven't taken statistics yet, but as a matter of interest I was contemplating the fact that uniform random variables added together seem to generate "bell curve" like distributions. My question is if I add up an infinite number of equally distributed random variables will the...

Homework Statement What is the relationship between the weight of the hanging washers and the force acting on the stopper by the string? Here is the diagram provided by the book: http://www.goodreads.com/photo/user/5034346-kylaia-formerly-known-as-klymene?photo=454140 It also says to...

Homework Statement f_{n} is is a sequence of functions in R, x\in [0,1] is f_{n} uniformly convergent? f = nx/1+n^{2}x^{2} Homework Equations uniform convergence \Leftrightarrow |f_{n}(x) - f(x)| < \epsilon \forall n>= n_{o} \inN The Attempt at a Solution lim f_{n} = lim...

Homework Statement A container in the form of a rectangular prism measuring 2m by 3m by 4m is covered with a layer of lead shielding of uniform thickness. Model the volume of the shielding as a function of its thickness. Treat the shelding as a hollow rectangular prism. DO NOT SIMPLIFY...

Homework Statement A straight wire, of current I, radius a is centred at (α,β). What are the x and y components of the magnetic field B inside one of the wires? Homework Equations ∮B.dl = μ I_enc ∫∫J.dS = I The Attempt at a Solution Any point (x,y) in the wire has a constant...

Homework Statement A uniform rod AB of weight W rests in equilibrium with the end A in contact with a smooth vertical wall and the end B in contact with a smooth plane inclined at 45 to the wall. Find the reactions at A and B in terms of W. Homework Equations The sum of the three forces equal...

Homework Statement Show that the gravitational field due to a horizontal uniform thin disc (thickness D, radius R and density r) at a distance h vertically above the centre of the disc has magnitude 2πGρd(1-h/(R2+h2)1/2) A pendulum clock in the centre of a large room is observed to keep...

Hey guys, I am thinking about world at small scale and world at larger scale. Why world is more chaos at smaller scale and why it is more smooth and uniform in larger scale?

Homework Statement The Bohr model of the hydrogem atom has one electron rotating around its center. If it has a radius of 5.29 * 10-11 m. And the mass of the electron is : 9.11 * 10-31. And the electrostatic force between the orbiting electron and the center proton is 8.20 * 10-8. Find: 1)...

Homework Statement A delivery truck wants to speed up its deliveries by dropping its packages into moving trucks. A worker is positioned in an overpass directly above a straight, level road to drop the packages into the truck at the correct time. One day, a delivery truck starts from rest and...

Homework Statement Let f,g be continuous on a closed bounded interval [a,b] with |g(x)| > 0 for all x in [a,b]. Suppose that f_n \to f and g_n \to g uniformly on [a,b]. Prove that \frac{1}{g_n} is defined for large n and \frac{f_n}{g_n} \to \frac{f}{g} uniformly on [a,b]. Show that this is...

Homework Statement A penny is flipped until we see the first head, and flips are assumed to be independent. For each tail we observe before the first head, the value of a continuous random variable with uniform PDF over the interval [0,3] is generated. Let the RV X be the sum of all the...

Homework Statement The prototypical electric dipole is made of two equal and opposite charges of magnitude q separated by a constant distance d (for example, the charges can be placed at opposite ends of a length d rod). The dipole is placed in a uniform, external electric field Er = E0 yˆ ...