Disk Definition and 783 Threads

$$Q=\int_{0}^{R} \left(\frac{a}{x} \times 2\pi x \right)dx$$ $$=2\pi aR$$ But the answer key is ##4\pi aR##. Where is my mistake? Thanks

Good afternoon! I would like to understand how the Faraday disk works and get answers to two questions. The working conditions are as follows: 1) we rotate the external circuit with a voltmeter relative to a stationary disk; 2) the external circuit is not in a magnetic field. Questions: 1) will...

This comes from Griffiths' Electrodynamics and is problem 2.51 or 2.52, the disk has a surface charge density and my usual approach to solving these problems is to pick an area element and find a way to create a vector to the point(s) at which the potential is evaluated at. I sent a picture of...

I'm asked to find 2 things: 1) The minimum value of the velocity ##v_0## that allows ##m## to complete a full revolution around the disk 2) the value of the pulse provided by the pin to the disc at the moment of impact. My thinking: I don't understand why the problem asks me to find a minimum...

The original question was to find the final velocity after falling from the height ##H## In many correct solutions to this problem, they consider the current density between the two surfaces to be ##\displaystyle J=\frac{1}{\rho } .\mathbf{E^{*}} =\frac{\mathbf{v} \times \mathbf{B}}{\rho }##...

I need to find ##v_1## and I know what are the initial conditions: ##\theta(0)=\pi## and ##\dot{\theta}(0)=0##. Then what is ##v_1## and how to find it? Thanks!

Hi! I am a very lost physics student here. I got a) but I have no idea how. The formula I used was from an online source and it was: I think I need a contextual explanation of this formula before I attempt b). My understanding of electric potential is that it is NOT potential energy, but...

I was able to solve first part I.e. time period of the system when bearing has friction I am unable to figure it out why disk will not rotate when it is mounted to frictionless bearing ? I know that due to absence of friction disk cannot rotate but then Mg is also there which can rotate the...

I want to find the cumulative mass m(r) of a mass disk. I have the mass density in terms of r, it is an exponential function: ρ(r)=ρ0*e^(-r/h) A double integral in polar coordinates should do, but im not sure about the solution I get.

In the frame of the patch ##-(1/\rho) \nabla p = - \nabla \phi##, and putting ##\nabla p = (\partial p/\partial \rho) \nabla \rho = c_s^2 \nabla \rho## and taking the ##z## component gives\begin{align*} -\frac{c_s^2}{\rho} \frac{\partial \rho}{\partial z} = -c_s^2...

Forces on rotating disk object Hi. Is it convenient to ask following question. Suppose we have solid circular object and 5 different moments like in the picture:In moment 1 we apply force (downwars direction) so as to start rotating the object around center of the mass (green dot) , Only...

I believe I've solved this problem, however, I got through it pretty quickly and since it's the last problem on the assignment, I feel that I may have had an oversight. For part a, I got: fs=md(α^2)(t^2) and for part b, I got: ω=Sqrt((µs*g)/d) Could someone confirm my answers? I've attached a...

I integrated B within the limits of a (from 0 to 0.007) teh result was 3.64E-10 T and it was wrong. the correcto one would be 5.8 E-4 T and it is a major diference (aprox 1 million times ) Waht shoud I have done? Regards

Hello, This question, which I found in various electricitiy and magnetism books (e.g. Introduction to electrodynamics grif.). There are many variations of this question, I am mainly interested in the following setup of it: -Suppose there is a charged disk of radius R lying in the xy-plane, and...

The situation is as follows. We have two disk magnets. One is fixed on the ground, table, or surface and has the north pole facing up. Then we have a metal plate fixed on the vertical axis rod or something similar such that it can't move up or down, but only rotate horizontally with as less...

The electric field strength at the center of a uniformly charged disk should be zero according to symmetry of concentric rings about the center, where each ring is contributing to the electric field at the center of the disk. For a thin ring of uniform charge distribution the formula is ##E =...

Let ##R=\sqrt{x^{2} + y^{2}}##. Then \begin{align}v_{tangential}&=\frac{dR}{dt} \nonumber\\ &=\frac{dR}{dx}\frac{dy}{dt} + \frac{dR}{dy}\frac{dy}{dt} \nonumber\\ &=\frac{x}{R}\frac{dx}{dt} + \frac{y}{R}\frac{dy}{dt} \nonumber\\ &= cos\phi \frac{dx}{dt} + sin\phi \frac{dy}{dt}.\nonumber...

Hi! For this problem, Why is the area of each ring segment dA equal to (2π)(r)(dr)? However, according to google the area of a ring segment (Annulus) is, Many thanks!

Just yesterday evening I saw a video of a few minutes where metal disks with holes in them were let fall into a basin of water.The water went up in twisted columns and made the most astounding and beautiful patterns. I thought I would show it to other people who might be interested - but I have...

Since the question made no indication of the disk rotating about its center, I just straight up assumed that the disk did not rotate about its center, and instead treated it as a point mass. However, to my surprise my calculations did not bear me any fruit. Below is my first attempt at the...

This was how the solution was arrived in the text, Net torque = F block x d block x sin ϴ0 + F rod x d rod x sin ϴ0 - T R sin 90 0 = 2mg x 2R x sin ϴ0 + m x R x sinϴ0 - T R T = 5 mg sinϴ0 I'm wondering do we have to resolve the forces for rod and block in to...

So, when the mass reached the peak, its horizontal velocity will be the same as the wedge's. Using conservation of momentum : $$ mu = 2mv$$ $$v = \frac u 2$$ With v is the final velocity for both objects. Now, what we need is the acceleration of the wedge, which we can find by using Newton's...

(a) By setting up a coordinate system with the x-axis pointing to the right and the y-axis pointing downward we have ##\begin{cases}-kx_{eq}+T_1+F_{s}=0\\ -RF_{s}+rT_1=0\\ r_p (T_2-T_1)=0\\ -T_2+mg=0\end{cases}\Rightarrow x_{eq}=\frac{mg}{k}\left(1+\frac{r}{R}\right)## which coincides with the...

I am using the following formula to solve this problem. $$ L_a= L_c + \text { (angular momentum of a particle at C of mass M)}$$ Because the point C is at rest relative to point A, so the second term in RHS of above equation is zero. Hence, the angular momentum about A is same as angular...

I have come up with two different approaches, but I'm not sure which one is correct since they give different answers. We use the following equation to get the total moment of inertia. ##I_o## = moment of inertia of disk about O axis + moment of inertia of road about O axis Approach 1...

Obviously, a third observer who is at rest with respect to the disk will see that the clock on the outside has a much faster velocity than a clock on the interior of the disk, so clearly the outside clock will show that it has measured less time. But that's one question. What about looking at...

I'm after a piece of (preferably free) software, or even a built in Windows 11 Home tool, that will log disk usage throughout the day, and what processes and application are using the disk, when, and by how much. For far too long now, I notice my laptop get into a frenzy of being at 100% disk...

Picture a flat disk of radius r with a radial vane. The disk is rotating at angular velocity w. Assume the vane is straight, starts at the center and ends at the perimeter of the disk. A very small round mass ( of m grams) is dropped onto the disk very near the center. The vane contacts it and...

Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?

The summary says it all, really, but in addition, I've done a lot of googling and am finding it hard to identify trustworthy options. LibreCrypt, DiskCryptor and VeraCrypt are candidates, but I have not used any of these tools so am wary of jumping in and finding that I have bricked my PC.

1) Since the rod is uniform, with mass m and length l, it has a linear mass density of ##\lambda=\frac{m}{l}##, so ##I_{rod_O}=\int_{x=r}^{x=r+l}x^2 \lambda dx=\frac{\lambda}{3}[(r+l)^3-r^3]=\frac{\lambda r^3}{3}[(1+\frac{l}{r})^3-1]=\frac{1}{3}mr^2[3+\frac{3l}{r}+\frac{l^2}{r^2}].##...

figure 11.12 I need someone to explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?p.s. ##\Delta\vec{L}_{total} = \vec{L}_{f} - \vec{L}_{i} = (-rm_{d}v_{df} +...

Greeting (x-3/2)^2+y^2=1/4 x^2+y^2-3y+9/4=1/4 r^2-3*r*sinθ+2=0 Δ=9sinθ^2-1 r=[3rsinθ-sqrt(sinθ^2-1)]/2 is my approch correct? thank you!

Question: Here's my attempt with the relevant equations: The correct answer is F = -99.4 az μN. Could someone please figure out my mistake?

In my job, I was given the task of calculating a force that operates an ultrasound transmitter on a receiver. The calculation is made by assuming that each point on the transmitter is a small transmitter and integration should be made on the surface of the transmitter. Since the transmitter is...

I am interested in particular in the second integral, in the ##\hat{r}## direction. Here is my depiction of the problem: As far as I can tell, due to the symmetry of the problem, this integral should be zero. $$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$ I don't believe I need to...

1) By conservation of linear momentum: ##m_1 v_1-m_2v_2=(m+m_1+m_2)v_{cm}\Rightarrow v_{cm}=\frac{m_1}{m+m_1+m_2}v_1-\frac{m_2}{m+m_1+m_2}v_2=\frac{3}{8}\frac{m}{s}##; 2) By conservation of angular momentum: ##-Rm_1v_1-Rm_2v_2=I_{total}\omega=(I_{disk}+m_1R^2+m_2R^2)\omega## so...

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Hello, reading the wiki entry for Langevin observers on rotating disk - Born_coordinates I'm struggling with the following quoted sentence: But as we see from Fig. 1, ideal clocks carried by these ring-riding observers cannot be synchronized. I do not grasp why, starting from the figure...

Question : Solution attempt : for

Good morning, I got a question like this- "A hard drive has 6 platters, each platter records data on both sides. There are 3000 tracks of nine sectors each. Each sector stores 512 bytes of data. How many read/ write heads are there and what are the capacity of the drive(in Gigabytes)?" I...

First, I tried to model the disk-bar as a crank connecting rod, to the OA bar, and apply this: VP = VB + ω_BP x r_P/B, where P is the contact point between the disc and OA bar. I assumed VP = VP sin 30º i + VP cos 30º j (direction parallel to r_P/B), where r_P/B = sin 30º i + cos 30 j This...

I have been given an answer for this but I am struggling to get to that point $$ANS = 0.430\, kg \cdot m^2$$ So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R##...

m = 60kg, ω0 = 2.094 rad/s, I of disk = 130 kgm^2 , outer position ro = 1.5m, inner position ri = 0.3m ∴Fifth object : Ffriction = m.ac μ.m.g = m. v^2 / R => vmax = √ 3. (1.5m) . (9.81 m/s^2 ) = 6.64 m/s => ωmax = 4.43 rad/s so when the fifth object move with greater speed than vmax...

I could do the first part of the question with ease but second part I am not sure how to proceed. Should we calculate the magnetic field at d(where the loop is) and infer something from that for it's motion?? Plz help me out Thanks in advance

Goodd day, I have a question regarding an exercice I have already posted Bvu was very nice and provided this darwing I already have the solution But y question is : can we use the disk method? because as you can see even though the intersection was at x=-1 the sphere goes deep into the...

Good day I have the following exercice and it's solved using spherical coordinates I totally agree with the solution but I have issue to find out why mine does not work I used the the integration by disk I divided the region of integration to 2 A1 and A2 (A2 is the upper half sphere and A1 is...

The age of the Nebra (from Germany) Sky Disk (claimed to be the oldest known representation of the heavens) is in dispute. It was found in the black market, so provenance is unclear. NY Times article here.

For a planet to be able to support life, it needs to have a source of energy. In our case this energy comes from the sun. But in this paper, the author argues that a rogue planet (a planet that has been ejected from its stellar system and no longer orbits any star and is wandering in...