Uniform Definition and 1000 Threads

Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...

Homework Statement ##I## a set of real number and ##f_k : I \rightarrow \mathbb{R}## a succession of real functions defined in ##I##. We say that ##f_k## converges punctually in ##I## to the function ##f : I \rightarrow \mathbb{R}## if $$\lim_{k \to \infty} f_k(x) = f(x), \hspace{1cm} \forall x...

Homework Statement A thin uniform rod of length l and mass m is constrained to rotate with constant angular velocity omega about an axis passing through the center O of the rod and making an angle alpha with the rod. a) Show the the angular momentum L about O is perpendicular to the rod and is...

Homework Statement A uniform chain lies in a heap on a table. If one end is raised vertically with uniform velocity v, show that the upward force that mus be exerted on the end of the chain is equal to the weight of a length z + (v^2/g) of the chain, where z is the length that has been uncoiled...

:H:H:H1. Homework Statement Homework Equations equations is not needed here The Attempt at a Solution I have no idea :( Please help me![/B]

ηϖ1. Homework Statement Homework Equations I=½MR2 PE=mgh The Attempt at a Solution The first thing that jumped out at me was "uniform cylinder" so I went ahead and calculated the moment of inertia for the cylinder and got I=½(4.4)(.4)2 = .352 and held onto that. Then, I calculated the...

Question :- A car has to move on a path, that is a arc of a circle of radius (##R##). The length of the path is (##L##). Suppose it starts on the highest point of the path, find the highest uniform speed for which, it does not lose contact with the path on any point ? My attempt :- I made a...

Homework Statement A stone tied to a string with length 1.10 m is whirled in a circle both horizontally and vertically with the same constant speed. In the vertical case the maximum tension in the string is 15.0% larger than the tension that exists when the string was horizontal. Determine the...

Homework Statement 1. A car is safely negotiating an unbanked circular turn at 21 m/s and the maximum static force acts on the tires. Suddenly a wet patch on the road reduces the static frictional force by a factor of three. At what speed must the driver slow to in order to safely continue on...

Homework Statement "Figure 8-32 shows a pendulum of length ##L=\frac{5}{4}m##. Its bob (which effectively has all the mass) has speed ##v_0## when the cord makes an angle ##\theta_0=40°## with the vertical. (a) What is the speed of the bob when it is in its lowest position if...

Homework Statement Imagine a particle with charge +Q moving with constant horizontal velocity passing perpendicular to electric field between two parallel plates. The length of the plates is L. Therefore, is the time spent in the field (well, between the plates), simply the length/horizontal...

A particle travels srating with a initial speed u, with uniform acceleration a. Show that the distance traveled during the nth second is u+an-.5a. (b) if the particle travels 17m in the 2nd second of motion and 47m in the 7th second of motion how far will it go in the (i) 10th second of motion...

Homework Statement Describe semiquantitatively the motion of an electron under the presence of a constant electric field in the x direction, E =E0x^ and a space varying magnetic field given by B = B0 a(x + z)x^ + B0 [1 + a(x - z)]z^ where Eo, Bo, and a are...

Homework Statement The uniform rod mass m, length L falling into mass M. M is attacked with string k. Find the velocity u of system when the top of rod falling into M. Homework Equations I find this equation, but it seems wrong: Chose origin at equilibrium position. The rod has been divided...

how can a rectangular coil placed in uniform magnetic field have torque? Isn't torque the force on an object while its rotating? Will the coil rotate in a magnetic field? I don't understand.

Homework Statement At t = 0, an elevator departs from the ground with uniform speed. At time ##T_1## a child drops a marble through the floor.The marble falls with uniform acceleration g = 9.8 m/s^2, and hits the ground at time ##t = T_2##. Find the height of the elevator time ##T_1##...

Homework Statement Suppose the nonconducting sphere of Example 22-4 has a spherical cavity of radius r1 centered at the sphere's center (see the figure). Assuming the charge Q is distributed uniformly in the "shell" (between r = r1 and r = r0), determine the electric field as a function of r...

For a conducting sheet that is transverse to a constant uniform incident field, I believe the resulting total field would simply be the incident field doubled. I'm trying to figure out why this happens, preferably avoiding the method of images since I am using this to figure out how the method...

Homework Statement Problem given in the image attached. Uniform Magnetic Field : B Positive Charge : q Uniform Velocity : v Mass : m Charged particle enters the magnetic field making an angle θ with the plane perpendicular to the magnetic field. Width of the region of Magnetic field : d d <...

Homework Statement In the figure a nonconducting spherical shell of inner radius a = 2.07 cm and outer radius b = 2.51 cm has (within its thickness) a positive volume charge density ρ = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of...

Homework Statement A uniform disk of mass m and radius R lies in a vertical plane and is pivoted about a point a distance ℓcm from its center of mass in (Figure 1) . When given a small rotational displacement about the pivot, the disk undergoes simple harmonic motion. Determine the period of...

I'm a bit rusty on partial uniform loading on a pin. I want to find the minimum diameter a cold rolled steel pin has to be using a factor of safety of 2 with a loading of 25000 lbs. The pin in the picture is welded between two plates (the right plate bends in and is welded to the left plate...

1. A uniform bar AB of length 3 m and weight 40 N rests in equilibrium with the lower end A on a smooth plane inclined at an angle alpha to the horizontal, where tan alpha = 3/4 and a point C of the rod against a smooth peg. If the rod makes an angle theta with the horizontal, where tan theta =...

1. A uniform right circular solid cone of weight W is suspended by two vertical strings attached to the ends A and B of a diameter of its base. If the cone hangs in equilibrium with its vertex vertically below A, find the tension in the strings. 2. Centre of mass of cone from the vertex is 3/4...

hi, There is a situation that if t^2-x^2=constant in minkowski space we have uniform acceleration(hyperbola). But, when I look at the derivation of this circumstance, the only thing I have found is: if there is a gravitational field uniformly, then we have uniform acceleration. But I can not...

How is Δθ in circle equals to angle in velocity vectors triangle? I tried using simple geometry but I can't.

FasterTrucks Ltd is a transport company. The enterprise needs to decide if a new delivery vehicle will be purchased. Two models are currently considered. You are required to indicate which one of the two models should be purchased. You decide to apply the method of EQUIVALENT UNIFORM ANNUAL...

Homework Statement A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring. https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif Its circular surfaces are horizontal. What effect will the...

Homework Statement Let ρ(r)= Qr/πR4 be the charge density distribution for a solid sphere of radius R and total charge Q.For a point 'P' inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is ? A) 0 B) Q/4πε°(r1)2 C) Q(r1)2/4πε°R4 D)...

Hello, Python,CFD and PF newbie here. I am using Spyder (Python 3.5) and I managed to plot my streamfunction in cartesian coordinates. I tried transforming and plotting in polar coordinates but I am not sure that what i have done is correct. I am not even sure what the plot should look like :/...

Let us have a continuous function f which is uniformly continuous on [a,b] and [b,c]... Then Spivak says, f is uniformly continuous on [a,c]... For prving this, he invokes the continuity of f on b... My questions here are: 1.For a given ε, we have a δ1 which works on whole of interval [a,b] and...

Hello, friends! The tridimensional version of the Biot-Savart law says that the magnetic field generated at the point ##\boldsymbol{r}\in\mathbb{R}^3## by a tridimensional distribution of current defined by the current density ##\boldsymbol{J}##...

Homework Statement A uniform rod of mass m and length L is freely pivoted at one end. What is the period of its oscillations? Icm for a uniform rod rotating about its centre of mass is 1/12mL2 (a) √3g/2L (b) 2π √3L/2g (c) 2π √2L/3g (d) 2π √L/g (e) none of the above Homework Equations ω2 =...

Homework Statement Several planets (Jupiter, Saturn, Uranus) are encircled by rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous thin ring of mass 2.1 x 1022 kg and outer radius 4.3 x 108 m (the...

Homework Statement A uniform beam of mass m is inclined at an angle θ to the horizontal. Its upper end (point P) produces a 90° bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (see figure below). Let μs represent the coefficient of static friction between...

Homework Statement Find the force that tries to rip apart a conducting shell into two halves about its equator when kept in a uniform electric field of magnitude ##E##. Homework Equations Gauss Law: $$\nabla\cdot\vec{E}=\frac{\rho}{\epsilon_0}$$ I think Laplace equation might also be...

Hello; I'm struggling with pointwise and uniform convergence, I think that examples are going to help me understand Homework Statement Consider the Fourier sine series of each of the following functions. In this exercise de not compute the coefficients but use the general convergence theorems...

This might be a stupid question due to a simplistic under standing of the Big Bang. But why is the CMB uniform across the sky. Why is it not sognificantly higher on one side from the other. Surely if the Big Bang was a point then everything would eminate from that point resulting in one side...

Let $X\sim U(0,1)$ and define $Y=1-X$. What statement is TRUE? (1): $F_{X}(u)\neq F_{Y}(u)$, for every $u\epsilon \left [ 0,1 \right ]$; (2): $Y$ is not a rv; (3): $E(X+Y)=2$; (4): $Y\sim U(0,1)$; (5): none of the remaining statements.

Homework Statement Homework Equations radial acceleration = v^2/R The Attempt at a Solution I'm unsure if we have to mention the tension of the cable, but I'm guessing L2 will suffice? Correct me if I am wrong. Anyways, I drew the diagram from a side view (kind of like a circular pendulum)...

Homework Statement A ball with a mass of 3.0 x 10-4 kg hangs from a 15 cm long thread between two parallel plates. The thread is deflected to the side, as shown in the following diagram. The charge on the ball is +5.0 x 10-5 C. a) Find the tension in the thread b) Find the magnitude and...

Homework Statement A ring of diameter 7.90 cm is fixed in place and carries a charge of 5.20 μC uniformly spread over its circumference. How much work does it take to move a tiny 3.40 μC charged ball of mass 1.50 g from very far away to the center of the ring? Homework Equations V=(KQ)/r^2...

Homework Statement We have seen that a long solenoid produces a uniform magnetic field directed along the axis of a cylindrical region. However, to produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, one can use saddle coils. The loops are wrapped over a...

Homework Statement An object is launched horizontally from the highest peak on the Moon's surface. Calculate (a) the launch speed required so that the object travels completely around the Moon and returns to its original position, and (b) the time required to return to the launch point. Assume...

Homework Statement [/B]Homework Equations Poynting's Theorem S = 1/μ0 (E x B) Momentum = p = μ0ε0 ∫ S dτ The Attempt at a Solution My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the...

Is it possible to derive the standard normal distribution from using polar form p = r*e^(i*v) to distribute uniform points along the contour of a circle? I've read that it is possible to randomize points like that using X and Y values with normal distribution by normalizing each point, but I...

I have been working with some Herschel images and I am finding it difficult to extract the astronomical sources from the image. The image background is extremely non uniform so i am not able to differentiate between the background and the source. I used some tasks in HIPE like source extractor...

Hi, I'm developing a new bio reactor, which in this instance you can think of as just a perspex fish tank. But have come across an unusual requirement to apply a roughly 0.01T magnetic field across the volume of the tank with mainly water in it. No position in the tank can be less than 0.08T and...

Hi, I have been studying up on circular motion in the vertical plane and I am happy with all the math/theory that I have read explaining the normal force and weight force and the feeling of being "heavier" and "lighter". My question is about the top of the hill/ride, The forces acting on you at...

Hello, from time to time I got question in physics for which I can't readily find answers. I hope I can get answers here. Here is my current one: Usually textbooks state that space contracts in direction parallel to direction of motion. It sounds strange, because time changes uniformly, and as I...