Uniform Definition and 1000 Threads

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 ...

Solved, thanks :D

How do I determine whether the following sequences of complex functions converge uniformly? i) z/n ii)1/nz iii)nz^2/(z+3in) where n is natural number

Hello everyone, I'm trying to read an economics paper on competitive auction pricing and I'm still coming up to speed with some of the concepts. As the title says, why is the clearing price of a uniform price auction the S + 1st highest of B buyers values? In this case each Seller has...

Homework Statement Write an equation for one component of the position vector as a function of the radius of the circle and the angle the vector makes with one axis of your coordinate system. Calculate how that angle depends on time and the constant angular speed of the object moving in a...

does it have uniform velocity?

or...?

Homework Statement a train starts from station a with a uniform acceleration of 5.00 x 10^-1 m/s^2 (east) and attains full speed after 50.0s. It travels at full speed for 1.20 x 10^2 s, then is brought to rest at station b by the application of the brakes which produces a constant...

Homework Statement A circular-motion addict of mass 82.0 kg rides a Ferris wheel around in a vertical circle of radius 14.0 m at a constant speed of 7.10 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b)...

What is "linear acceleration" in uniform circular motion? Yesterday, I took an exam and it was asked a concept that we hadn't studied, at least in the way it was written. The exercise explained that a circular motion was decreasing its velocity, and we had to be able to identify which of the...

Homework Statement a single loop of wire with radius A is rotating in a uniform magnetic field at angular frequency ω. The loop of wire drives a current through a resistor R. Determine the torque as a function of time needed to turn the wire. Homework Equations 1) Emf = ∫Fmag.dl...

Hello!A little problem:With the given series,$$Y(x)= \sum_{n=1}^{\infty}(-1)^n\frac{x^n\ln^nx}{n!} $$ ,why $Y(x)$ is Uniformly converges for all $x\in(0,1]$ ?Ok, I know that $Y(x)$ is u.c by M-test: $$\max{|x\ln{x}|}=\frac{1}{e}$$ And, $$ \sum_{n=0}^{\infty}\frac{(\frac{1}{e})^n}{n!} $$ Is...

Hey guys, I have a bunch price observations. I would like to know whether some subset of my observations is uniformly distributed (or close to being uniformly distributed). How could I go about testing this? Thanks.

A 20-cm radius ball is uniformly charged to 80 nC. (a) What is the ball’s charge density (C/m3)? (b) How much charge is enclosed by spheres at points 5, 10 and 20 cm from the center? (c) What is the electric field strength at points 5, 10 and 20 cm from the center? ATTEMPT: part a: i...

Homework Statement If R1 and R2 are two uniformly distributed random variables on the interval [0,1]. What is the density function Z=R1*R2? Homework Equations I'm not sure actually The Attempt at a Solution I have tried to manipulate with moment generating function (which i...

Homework Statement I have a solid cylinder of uniform charge density whose axis is centered along the z-axis. I am trying to calculate the electric field at a point on the z-axis. What I'm trying to do is to start by first calculating the field of a disk centered on the z-axis at a point on...

Homework Statement A uniform sphere rolls down a 30 degree incline θ from height h. Initially, the solid is at rest. Find the acceleration for the center of the mass of the solid. I am not sure where to start with this problem. I started with the energy formulas, but I am not sure how to find...

A solenoid, of sufficient length to consider external flux to be zero, passes through a uniform magnetic field with significant length on both ends extending beyond the field. Will a torque be exerted upon the solenoid ? Or do the windings effectively mask the internal solenoid field from the...