Cylinder Definition and 1000 Threads

Homework Statement Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry. Homework Equations $$dm = \rho dV$$ $$dV = (2 \pi R)(dR)(h)$$ The Attempt at a Solution I was mainly...

Homework Statement With the equations of motion in polar coordinates given by ##r(t)=pcos{kt^2}, φ(t)=kt^2## determine the velocity intensity of a point ##M## on the circumference of a cylinder which is rolling without friction on a horizontal plane at time ##t## is the velocity of the center...

The general formula to calculate maximim electric, Emax in concetric cylinder is Emax= V/a ln (b/a). But how does the formula differentiate if there are 3 inner cylindrical electrode?

The axis of the cylinder is perpendicular(not parallel) to M, magnetization. It's not hard to find bound surface current density, but it depends on the angle while the answer says the magnetic field is uniform inside the cylinder. Anyone can silve this problem??

Homework Statement A viscous liquid with density and viscosity ##\rho## and ##\mu## respectively is discharged onto the upper surface of a cylinder with radius ##a## at a volume flow rate ##Q##. This is a gravity-driven flow, and it forms a film around the cylinder--see picture. What is the...

1. The problem stsatemesnt, all variables and given/known data A cylinder conductor of length ##l##, inner radius ##a## and outer radius ##b## is half-filled with a liquid dielectric as shown in the picture. The cylinder is attached to a battery of constant voltage ##U## and then separated from...

Homework Statement For a given system, a conducting cylinder with radius ##r=a## with a linear charge density ##Q'## and a conducting surface at a distance ##z=h## from the cylinder, calculate the linear capacitance of the cylinder.Take that ##h>>a## ##C'=\frac{Q'}{U}## Homework Equations 3...

Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...

I know that the surface roughness plays an role in the Magnus force exerted of a rotating cylinder. But, i cannot find an equation that includes the surface roughness in the equation of the Magnus force. If someone could state the formula (and preferably a source to read up more on it) it would...

Homework Statement Metal cylinder of radius a has the z-axis as its symmetry. It has magnetic field at any point P as: $$B[x,y,z] = \frac{1}{2} \mu_0 J_z [-ye_x + xe_y]$$ A cylindrical hole of radius b which is displaced from the cylinder's axis by d in the x direction. The magnetic field...

Homework Statement Find the volume of solid bounded below by plane z = 0 , and above by z = 10 , sides by (x^2) + (y-1)^2 = 1 .. Homework EquationsThe Attempt at a Solution I fins the area of the base first , which is pi (1^2) = pi , then i integrate with the length , which is from z = 0 to...

Homework Statement Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b. Set up an iterated integral for the volume of W Homework Equations x^2+y^2+z^2=b^2 x^2+y^2=a^2 0<a<b The Attempt at a Solution I converted to cylindrical coordinates...

Homework Statement Homework Equations The Attempt at a Solution Because we are only looking at a cross section, I tried to reduce 5.3 down to just being a function of R and Theta. However I reasoned that there should be, based on this problem, no dependence on Theta either, so I figured I...

Homework Statement We have an infinite cylinder that, from radius 0 to a, has a volume current density ##\vec{J(r)}=J_{0}(r/a) \hat{z}## , then from a to 2a, it has a material with uniform linear magnetic permeability ##\mu=(3/2)\mu_0## , and at the surface, it has surface current...

Homework Statement I have a system of two ordinary differential equations as shown below. I have to prove that the Lame's exact solutions for a thick walled cylinder loaded by internal pressure satisfies the equations. The next step is to integrate the equations to obtain an equation for U...

Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...

There is this bike manufactured in India with a 180CC single cylinder petrol engine with Twin Spark plugs. They highly market their "twin spark technology". Well according to my knowledge, I don't think that will make much difference in performance and efficiency. What do you think? Is this just...

Homework Statement [/B] Begin with a solid cylinder of mass M and radius R. A hole is bored through this cylinder with radius r < R/2, parallel to the axis of the cylinder and with the surface of the hole touching the cylinder’s axis. This modified cylinder then rolls on a horizontal surface...

Hi all, In this article, page 7 - 3 there is a drawing of a Cylinder suffering Torsion. In the next page it says: ftp://www.bauwesen.fh-muenchen.de/Bauwesen/Konrad/Baustatik_1/Festigkeitslehre/kap07.pdf γ⋅dx = r⋅dϑ From my observations i come to tan γ=s/x ; tan ϑ=s/r ; therefore x⋅tan γ =...

Homework Statement A long copper rod 8 cm in diameter has an off-center cylindrical hole 4 cm in diameter down its full length. This conductor carries a current of 900 amps flowing in the direction “into the paper.” What is the direction, and strength in tesla, of the magnetic field at the...

Homework Statement By using cylindrical coordinate , evaluate ∫ ∫ ∫ zDv , where G is the solid bounded by the cylinder (y^2) + (z^2) = 1 , cut by plane of y = x , x = 0 and z = 0 I can understand that the solid formed , was cut by x = 0 , thus the base of the solid formed has circle of (y^2) +...

Homework Statement A cylinder having a mass of 5.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure: F1 = 5.0 N, F2 = 6.0 N, F3 = 2.5 N, and F4 = 5.5 N. Also, R1 = 6.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the angular...

Hi, given an Hydraulic Cylinder with the Formula: F=p*A Why do we use APiston to calculate the Force in Work-Direction? Doesnt it suppose the "Potential Energy" of the compressed air just presses in that Area? Im pretty confused, sorry about the unconcrete question.

Homework Statement Julia plans to make a cylindrical vase in which the bottom of the vase is 0.3 cm thick and the curved, lateral part of the vase is to be 0.2 cm thick. If the vase needs to have a volume of 1 liter, what should its dimensions be to minimize its weight? Homework Equations...

Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...

Homework Statement Homework Equations Vab = ∫ E*dr The Attempt at a Solution [/B] For part (b) I am not sure if I should set the upper and lower bound of the integral from "R" to "2R" or "2R" to "3R". If done so, this would give me V2R = Vab * ln|3R/2R| / ln |3| instead of what is on the...

While I was studying with electric field about cylinder, I learned that for a very long cylinder, the electric field in the hollow of cylinder will be zero. http://physics.stackexchange.com/questions/156789/electric-field-of-hollow-cylinder However, I couldn't accept this intuitively, and...

Homework Statement WITHOUT using Gauss's law calculate the electric field at all points outside and inside an infinite cylinder with circular cross section of radius b and charge density ρ Hint: Use cylindrical coordinates and place the target charge on the x axis..Homework Equations E =...

Homework Statement [/B] Calculate the volume bounded by the plane/cylinder x^2+y^2=1 and the planes x+z=1 and y-z=-1. Homework Equations / The attempt at a solution[/B] It is pretty basic triple integral in cylindrical coordinates. For some reason, I can't get the right answer. I'm using...

Hi I'm working on a project out in the North Sea on an oil rig, we need to remove a hydraulic cylinder from a crane, I have attached a drawing the red cylinder B needs to be removed. To do this we will move the crane boom to the position shown by the orange lines and rest the end down on the...

Hi, are there any experimentalists here? I have gas in a cylinder. I have just been taking samples of gas from a tube connected to the outlet, but air is getting in the syringe. So I went over to chemistry and got a round bottom flask with 3 inlets / outlets and a septum, so its like this: I...

Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc... 1. Homework...

Hello. Here is my problem: I want to mount 2 solar panels on a horizontal 10 foot bar. (panels are 5' and 20-40/lbs each - so 80lbs) is there a formula i can use on each material option to figure out what material to use for the 10 foot bar (what won't break under the weight of the panels or...

Homework Statement An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high...

Homework Statement In a vertical piston cylinder assembly, a vertical shaft whose cross sectional area is 0.8 cm^2 is attached to the top of the piston. Determine the magnitude F, of the force acting on the shaft, in N, required if the gas pressure inside the cylinder is 3 bar. The masses of...

Hi There, I am trying to understand if I have a vacuum in the below scenario or simply just really low pressure. A pump supplies a pipe with a constant supply of water at one end (Point A) the water discharges several kilometers away at some lower elevation (Point B). At "Point A" a valve...

it is given that the perimeter of the rectangle is (80 + 120 + 80 + 120) = 400 cm From this you need to make a cylinder with maximin volume: 400 = 2r + 2h 2h = 400 - 2r h = 200 - r . We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER V = πr^2 h However, before we differentiate the...

Hello, I have recently bought 4 cylindrical lithium ion batteries from hobby king to make a battery pack. To do this, I put all 4 of them in Parallel, so that the voltage would stay the same, but the capacity would increase. It says on Hobby king that they can charge at 5C, and since they are...

Hello! We have a solid cylinder and then we take that and drill its core so that it becomes hollow. In which case the cylinder will be stronger? Thanks!

Please solve this problem :)

Homework Statement [/B] A cylinder with mass 3kg slides on ice with its base surface at 5m/s and collides with an identical but stationary cylinder. The collision is elastic. After the collision, the center-masses of the cylinders move at angles 45 and 30 degrees from the starting direction...

Homework Statement This is a problem from Spacetime and Geometry by Carroll, Just because a manifold is topologically nontrivial doesn't necessarily mean it can't be covered with a single chart. In contrast to the circle ##S^1##, show that the infinite cylinder ##RxS^1## can be covered with...

Homework Statement Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the...

Homework Statement At the height h, from the top of inclined plane forming an angle α with the horizontal, a disk slips down which has radius R, thickness d, mass m and resistivity ρ. On inclined plane, an area S is very small square that has a magnetic field B. The magnetic field B is...

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...

Can anyone recommend a good (peer reviewed) reference that discusses low Reynolds number flow around a cylinder? I'm specifically looking for derivations of the drag coefficient. The usual 'gold standard' references...

Hello, according to thermodynamics the compression of a cylinder can both increase pressure and increase temperature. Unfortunately there is no law that gives us boh presure and temperture change given the change of volume, previous temperature and previous pressure? Usually we do either assume...

Homework Statement A cylinder of mass m and radius R is set on a plane, with large enough friction coefficient to ensure at any moment rolling without slipping. A constant torque is applied along the axis passing through the center of mass (G) of the cylinder and perpendicular to the basis of...

Homework Statement Homework EquationsThe Attempt at a Solution To bring the cylinder to a stop both linear impulse and angular impulse would be required . Linear impulse would be provided by the normal force from the plane whereas the angular impulse has to be provided by the frictional...

Homework Statement Evaluate ##\int\int_S \textbf{F}\cdot\textbf{n} dS ## where ##\textbf{F}=(z^2-x)\textbf{i}-xy\textbf{j}+3z\textbf{k}## and S is the surface region bounded by ##z = 4-y^2, x=0, x=3## and the x-y plane with ##\textbf{n}## directed outward to S. The attempt at a solution I've...