Homework Statement
A disk rotates with angular velocity w. Two masses, Ma and Mb, slide without friction in a groove passing through the cnter of the disk. They are connected by a light string of length L, and are initially held in position by a catch, with mass Ma at distance Ra from the...
Homework Statement
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = sec(x), y = 1, x = 1, x = -1 on the x-axis.
The Attempt at a Solution
This should be ridiculously easy but apparently my answer is wrong?!
To calculate the...
Hi,
I am trying to get my head around the Van Kampen Theorem, and how this could be applied to find the fundamental group of X = the union of the unit sphere S2 in R3 and the unit disk in x-y plane? I was thinking of splitting the sphere into 3 regions - two spherical caps each having open...
Turns out that my HDD and SSD are badly fragmented as they have never had a defrag run on them in more than two years. So someone recommended that I run a disk defrag.
What exactly does this do? Will it make my computer run faster?
Homework Statement
First of all can i say that my question is part of a bigger problem that I'm trying to solve, but for the moment I'm stuck at this bit!
I'm trying to obtain a function that will return the temperature at a chosen point (r,\theta) on a disk of radius r_{0}. The...
Hi, I was just wondering, why are we only looking for massive compact HALO objects?
Can there not be such objects in the Galaxys disk, if so why? Or have simply already detected all of them, if so how?
Let f(x) be a function which is defined in the open unit disk (|z| < 1) and is analytic there. f(z) maps the unit disk onto itself k times, meaning |f(z)| < 1 for all |z| < 1 and every point in the unit disk has k preimages under f(z). Prove that f(z) must be a rational function. Furthermore...
I have a question about the electric field of a uniformly charged disk with radius a. I'll move point by point till i reach the part i really can't get. First of all, the surface area is made of infinite number of RINGS! So, we basically integrate the charge of the rings from r="0" to r="a"...
Homework Statement
I'm supposed to find the time taken for the disk to slow down from ω0 to (1/2)ω0...Here's what I've done:
Since on each side of the disk there is current flowing into the centre, each side experiences a force F, so the net torque on the system = 2Fa. Then I can find...
Hello,
I am looking at an example of finding the charge of a uniform disk with a continuous charge on the surface.
They go about the problem by finding the infinitesimal charge of concentric rings
dq = σdA = σ(2πr dr)
The part I don't understand is that they use the area as 2πr dr...
Homework Statement
A small disc or radius R with surface normal
ˆ
k is placed a distance z from a point charge −q,( k hat pointing along the z-axis which goes through the charge and the center of the disk.)
Assuming that R ≪ z, derive an expression for the electric flux ΦE passing through...
Homework Statement
The parabola y=1/2 x^2 divides the disk x^2+y^2 <or= to 8 into two equal parts. Find the area of both parts.
Homework Equations
The Attempt at a Solution
I have no idea of how to go about solving this. We haven't done any application problems until now and when...
Homework Statement
The thing that is lying on the disk(Disko), is rotating together with disko. After the rotary frequency of disko grew twice (N X 2), friction(rubbing) Force grew F=6 ( F + 6). You have to understand friction Force module at the original frequency.
Homework Equations...
Homework Statement
taken directly from Rindler
A large disc rotates at uniform angular velocity ω in inertial frame S. Two observers O1 and O2 ride on the disc at radial distances r1 and r2. They carry clocks C1 and C2 they adjust to keep with clocks time with S, i.e., they have been adjusted...
Homework Statement
Determine how many integrals are required for disk, washer, and shell method.Homework Equations
x=3y^2 - 2 and x=y^2 from (-2,0) to (1,1) about x-axis.The Attempt at a Solution
Since there are no breaks or abnormalities in the graph it appears that 1 integral will solve for...
I began designing a clay disk launcher for when I go to a gun range and I want it to be something like this:
I am having trouble sizing an electric motor since I don't have much exposure to E.Eng.
The clay pigeon launcher is about 10cm by 10cm and I calculated my exit speed to be 20-35m/s...
Homework Statement
Hi,
I have a problem that describes a uniformly charged disk and the electric field a distance z from the center.
I have found an equation that describes the E field at any point z already. Now I have to find out how the E field decreases as z increases-- as 1/r^2...
A disk of radius 2.4 cm carries a uniform surface charge density of 3.1 μ C/m2. Using reasonable approximations, find the electric field on the axis at the following distances.
I have used the equation E=(Q/ε0)(1/(4*pi*r2))
I also tried the equation E=(Q/2(ε0))(1-(z/(√(z2)+(r2)))
Thanks...
Hi,
Homework Statement
A horizontal smooth disk of radius R rotates around its axis with constant speed ω. At t=0 a mass m is thrown at speed v0 (in the lab's frame of reference) towards the center of the disk.
I am asked to write down the velocity vector of the mass in the lab's frame of...
came across the concept of Frame dragging.
i cannot find if this phenomena also aids in addition to the conversation of angular momentum the formation of an accretion disk around neutron stars/black holes.
cheers
Homework Statement
A uniform metal disk (M = 8.21 kg, R = 1.88 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations.
Homework Equations
I = mr^{2}/4
T = 2\pi √(I/mgd)
The Attempt at a Solution
I combined the formula...
Homework Statement
Determine the relationship between the angular
acceleration of the flywheel, the downward acceleration of the block, and the radius of
the ring.
Known data:
Mass Ring: 1.420 kg
Radius Ring (Inside, then Outside): 5.10 cm, 6.325 cm
Mass Disk: 1.455 kg
Radius Disk...
In an X-ray binary system, in which one of the two objects is black hole candidate, there are several ways to exchange mass.
A paper states that" their host systems are mass-exchange binaries containing a nondegenerate star that supplies gas to the black hole via a stellar wind or via...
Homework Statement
Mass M is distributed uniformly over a disk of radius a. Find the gravitational force between this disk-shaped mass and a particle with mass m located a distance x above the center of the disk.
Homework Equations
The problem gives the hint to use the equation found in...
Homework Statement
I am trying to find the moment of inertia of a disc (let the mass be m and radius R) inclined at an angle θ to the vertical axis.
(See attachment 1)
Homework Equations
The Attempt at a Solution
I started by taking a small element of area dA. (see attachment 2)
The mass of...
Homework Statement
http://i.imgur.com/EhPmE.png
The pulley(disk) has a radius R and a mass m the rope does not slip over the pulley and the pulley spins on a frictionless axle. the coefficient of kinetic friction between block A and the surface is μk. the system is released from rest and...
What are they? I have some poeple telling me that for a cylinder it's I = (1/4)MR2 + (1/12)ML2 and that for a disk it's the same. Other people have told me that it's I = (1/2)MR2 for a disk and that it's the same for a cylinder. In the past I've used the former and have gotten the right answers...
1. Let’s say we have a solid wheel. The wheel can be modeled as a disk. Imagine that instead, the wheel is rotated at a location location 0.47R from the center of the wheel, so that the wheel rolled around a kind of loop. Essentially, the CM goes around the dashed line in the drawing. R is the...
Homework Statement
Use the shell method to find the volume of the area enclosed by:
y= 16-x^2 , y= 16,x=4, around y=16
Homework Equations
2\pi\int (shell height)( shell radius)
The Attempt at a Solution
I tried using the disk method and obtained \frac{1024}{5}*\pi
but I'm...
Homework Statement
When calculating moment of inertia of a disk there is something that really bothers me. I've googled this a lot and everywhere i look they 'assume' that the Δa = Δr*2∏r, formula for rectangle, not circle: (area of circle r+Δr - area of circle r) Δa = ∏(r+Δr)^2 - ∏r^2 = ∏r^2 +...
Hello,
it is well-known that with stereographic projection we can obtain a 1-1 correspondence between the points of the 2d Cartesian plane (plus the point at infinity), and the points on the Riemann sphere.
What is the geometrical construction that corresponds to a 1-1 mapping between the...
Homework Statement
I want to calculate the moment of inertia of a spinning disk via integration. I'm aware of the perpedicular axis theorem, but I want to integrate.
Homework Equations
I = ∫r^2dm
The Attempt at a Solution
if I set my coordinate axis op so that the origin of the...
OK, so I'm trying to build a hyper-fast rotating disk, probably of aluminum. The tensile strength is about 200MPa (note that this is a pressure, which makes sense), and I'm trying to calculate the tensile pressure throughout the disk. The point being to find out how fast I can spin the thing...
Homework Statement
f(z) is analytic for |z|≥1. Let C be the unit circle. Show that the integral \frac{1}{2i\pi}\int_C\frac{f(w)}{wz-z^2}dw is 0 if |z|<1, is \frac{f(z)}{z} if |z|>1
Homework Equations
The Attempt at a Solution
For |z|<1 case, I tried to write the integral as
\frac{1}{z2\pi...
[SOLVED]Angular Velocity of a Nebula Accretion Disk
[SOLVED]
According to astronomy our solar system was created about 4.5 billion years ago when the nebula of an exploded supernova accreted to form a stellar mass known as our sun.
They say that this "accretion disk" or mass of clumping...
This is my first attempt at imaging a debris disk around a star. I chose Fomalhaut because, as far as I can tell, there are no other stars visible at this time of year in the northern hemisphere with their disk's as widely separated from them as Fomalhaut.
This task is rather difficult...
Homework Statement
In what direction (using cylindrical coordinates) around a uniformly disk does the electric field NOT point?
Homework Equations
The directions could be r, θ, or z.
The Attempt at a Solution
I don't think it can point in the θ or the z direction-- either one would...
Homework Statement
A spherical charged ball of radius "a" has an empty spherical cavity, of radius b<a, at its center. There is no charge outside the ball and no sheet-charge on its outer surface. The (radial) field has given value Ea on the outer surface; inside the ball it is given as...
Homework Statement
A non-conducting disk with a 4-mm thickness is lying flat. It has a -4 C/m^2 surface charge on the upper surface and a surface charge on the lower surface. In terms of epsilon naught, what is the approximate field strength 1 mm above the upper surface?
Homework...
Homework Statement
A charged disk of total charge "Q" and radius "a" lies in the xy-plane, centered at the origin. The surface-charge density distribution is nonuniform, having the surface-density, at any point inside the disk at distance "r" from the center of the form
σ(r)= m x r^2 , m...
Hi can someone help me with this problem?
A thin disc of radius 60 cm has a hole its center of radius 30 cm. A total charge of
10^-3C is distributed uniformly on its surface. Find E at a point P which is 10 cm. on the central axis of this disc.
What would be the acceleration of an electron...
We all know that M.I of a Uniform rigid rod about an axis perpendicular to it's length and passing through it's center is MLsquare/12.Where M is mass and L is length of the rod. If it is broken to half such that M becomes M/2 and L becomes L/2,we can't apply ML square /12 formula to it.We have...
Homework Statement
We have an uniformly charged disk with total charge q, which is rotating around its axis with constant angular velocity w. Calculate electric and magnetic field in the axis and in the rotation plane. Calculate the radiated power in one cicle.
Homework Equations...
Homework Statement
A thin uniform rod is attached to an axis through its midpoint. The axis is standing on a disk rotating with constant angular speed \Omega about its symmetry axis. The rod's midpoint is located directly above the rotational axis of the disk. Let \theta denote the rod's...
Hello everybody.
I have to admit that I feel quite troubled since long time, actually since I read the solution of a problem that I don't understand and whose wording I immediately pass to briefly relate you. I guess that many of you have heard about the Faraday's disk, that is, a spinning...
Homework Statement
A cilindrical copper disk (radius R, thickness a) at time t=0 is spinning around its axis with angular speed w in a uniform magnetic field B parallel to its axis. The edge of the disk is connected to the center with a "wire" which we assume to have negligible resistance and...
Homework Statement
A disk begins spinning from rest with angular acceleration @ = 12 rad/s^2. A small object is on the disk a distance r = 2.0 cm from the center. What is the magnitude of the net acceleration of the object after a time t = 0.25s?
(alpha) @ = 12 rad/s^2
r = 2 cm
t = 0.25 s...
Homework Statement
A bullet with 5 g of mass and a velocity of 100m/s goes through a disk that was rested initially the disk is solid and as a radius r=20cm. It's 2cm thick and as a 2kg mass that can spin with no friction in an axis that goes through the center. The bullet goes trough the...
I am reading Thurston's book on the Geometry and Topology of 3-manifolds, and he describes the metric in the Poincare disk model of hyperbolic space as follows:
... the following formula for the hyperbolic metric ds^2 as a function of the Euclidean metric x^2:
ds^2 = \frac{4}{(1-r^2)^2} dx^2...