Circular Definition and 999 Threads

Homework Statement A stone tied to a rope rotates in a vertical circle. prove that the tension in the rope at the lowest point is 6 times the stone's weight bigger than at the highest point. Homework Equations Potential energy: E_P=mgh Kinetic energy: E_K=\frac{1}{2}mV^2 Radial force...

Hello experts! I am looking for the proof of the following equation: \frac{∂^{2}E}{∂r^{2}}+\frac{1}{r}\frac{∂Ez}{∂r}+\frac{1}{r^{2}}\frac{∂^{2}Ez}{∂ø^{2}}+q²Ez=0 I think this equation is somehow related to the cylindrical waveguides. Right? I am looking for it and I am unable to find...

Hello everyone, I'm really stuck on this question. The diagram shows an amusement park ride which contains a carriage attached to a mechanical arm. This arm spins around full circle. The carriage has a mass of 300 kg and a maximum occupancy of 300 kg. The question asks: With its carriage...

Homework Statement A small ball of mass 0.50 kg is attached to a cord and perform uniform-speed circular motion of radius 2.0 m in a vertical plane. i) If the speed of the circular motion is 10m/s, determine the tension in the cord at the lowest point of the circular motion. ii)...

Can someone Please explain to me how do these isolators works, i mean what about the parts? why does it look like this? and what's the purpose of the spring like thing around the isolators?

Homework Statement A chemistry lab centrifuge spins creating a circular trajectory for the solutes in the test tubes with a diameter of 20cm. If an acceleration of 10 times the Earth's gravitational acceleration is required, which of the following is a minimum frequency that must be...

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then it's volume is I keep on getting 18 root 3. But the answer is 36 root 3. Could I get some help? Thanks.

Hi everyone, my physics final is coming in 3 days:cry: , and I really need to have an answer to this exercise , but I'm stuck ! I don't even understand the problem statement HELP ! A typical fastball is thrwon at approximately 90 mph and with a spin rate of 113 rpm (I don't understand what it...

Homework Statement -I've attached a picture of the problem- An infinitely long straight wire of steady current I1 is placed to the left of a circular wire of current I2 and radius a as shown. The center of the circular wire is distance d(≥ a) away from the straight wire. Let’s find the net...

Homework Statement Show that the stability condition for a circular orbit of radius a, i.e. f(a) + \frac{a}{3} (\frac{df}{dr})_{r=a} < 0 is equivalent to the condition \frac{d^2V(r)}{dr^2} > 0 for r=a where V(r) is the effective potential given by V(r) = U(r) +...

Homework Statement A time t = 0 an electron enters a region of uniform magnetic field B = 0.010 T and has kinetic energy of 6.40E-16 J. It goes through a half-circle, exits the field and then accelerates across a gap with a potential difference of 2000 V, increasing in speed. It then hits a...

There is a cube with its sides equal to d and its thikness equal to t. It also has a circular hole at its center with radius a (a<<d). Two sides of the cube are maintained at potentials V_0 and -V_0 . I want to find the potential inside the cube but I see no way for obtaining the boundary...

Homework Statement What must be the period of rotation of the Earth on its axis so that a person at the equator will have a reading on the scale that is approximately one fifth as much as he would at the North Pole? (Given on the formula sheet) Radius of Earth = 6.37 x 10^6 m Homework...

Homework Statement Some kid is playing with a yoyo of mass m. The yoyo string is let out to length L, and is spun in a horizontal circle at a constant rate of ω. The yoyo string makes an angle of θ with the horizontal m = 39 grams = 0.039 kilgrams L = 46cm = 0.46m ω = 3 rads/sec...

Homework Statement A steel ball of mass m is fastened to a cord of length L and released when the cord is horizontal. At the bottom of the path, the ball strikes a hard plastic block of mass M = 4m at rest on a frictionless surface. The collision is elastic. Find the speed of the block...

Hi, if I have a mass on a string and I swing it around my head at a constant speed, what is the resultant force on the mass (I'm looking for a qualitative rather than quantitive answer)? My inital thoughts were towards the centre of rotation, due to the tension on the string (and since the...

A particle of 100 grams is attached by two strings of lengths 30cm and 50cm respectively to points A and B, where A is 30cm vertically below B. Find the range of angular velocities for which the particle can describe horizontal circles with both strings taut. Take g as 10m/s^2 Answer Show...

Homework Statement A circular steel plate of radius 15 cm is cooled from 350 C to 20 C. By what percentage does the plates area decorate ? Homework Equations A=∏r^2 Af = Ai (1+2∂ΔT) specific heat of steel = 12 x 10^-6 The Attempt at a Solution r = 15 cm = .15 m Ai = .070685 m^2...

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Could anyone help my with proving that the acceleration of an object that is moving with uniform circular motion is directed towards the centre of the circle and is of magnitude ω^2(r). Thanks

Suppose that we have a body that is moving at a straight line, inertially wrt to another frame. If it starts to move in a circular way after that, what can be said about the motions of its points. Do all points have to deccelrate to achieve the circular motion, but in a different manner, since...

1. The problem statement, ramp. variables and given/known data A block with mass m=5kg is placed at position A and given an initial velocity Va=2m/s Down a frictionless circular ramp. Between positions B and C it travels over a flat rough surface having a coefficient of kinetic friction...

I'm a little stumped with this problem, I have posted a photograph below as there is a diagram to compliment the questionExpressions which I used where V(r)= k q/r Where q= σ da Where da is an element of area And k= 1/4πεI messed around with these expressions for a while but it didn't really...

Hello everyone, I want to have a simple example of an inductance calculation. The magnetic field normal to a filamentary circular current loop is not constant over the circle but if we approximate the value as that for the center, multiply by the area of the circle and divide by the current...

Homework Statement Find the area of the region in the first quadrant, which is bounded by the x-axis, the line x = 2 and the circular arc x^2 + y^2 = 8Homework Equations The Attempt at a Solution I didn't use the hint given in the question but does my answer still makes sense. Did I set up the...

The question is to find the magnetic field at the centre of a current carrying circular loop of radius R, where the current = I Okay so I'm trying to do this by both Amp's Law and Biot Savarts Law, and I can't get my answers to agree. First method - Biot Savarts Law...

Hi Can someone tell me how to determine dimensions for a square hollow rod and circular hollow rod when the material and maximum load is known?

Homework Statement A ball of mass 125g is attached to a string .900 meters long. It is then set into vertical circular motion with 38 RPM. What is the tension of the string at the top of the circle and at the bottom of the circle? Homework Equations ∑Fy = may = marad arad = v2/R =...

Homework Statement I found this in Binney's text, pg 154 where he described the radial probability density ##P_{(r)} \propto r^2 u_L## Homework Equations The Attempt at a Solution Isn't the radial probability density simply the square of the normalized wavefunction...

Hey guys, first post here! Hoping to get a little help. Homework Statement You are a traffic safety engineer in charge of determining safe speeds for roads. A particular banked curve has a radius of 11.0 meters and is banked at an angle of 8.00°. The coefficient of static friction between...

Hello, I was asked to make experiments related to circular motion. The experiments will engage on different situations related to circular motion that we need to explain such as: -Analyzing the forces and the acceleration of a ball that moving circularly in a squared glass compared to the same...

Homework Statement Taken from Binney's Text, pg 143. Homework Equations The Attempt at a Solution From equation (7.36): we see that ##\delta a## is in the direction of the angle rotated, ##\vec{x}## is the position vector, and ##\vec{n}## is the unit normal to the plane of...

Homework Statement a passenger with height 175cmis driving on a city bus. The center of mass is at h=110cm above the middle point of the shoe which are 30 cm long. The passenger is standing in the direction of the ride. h=175cm h*=110cm shoe size = 30 cm b) the bus is driving in a circle...

What mathematical algebra explains sequence of circular shifts on rows and columns of a matrix? Consider a simple matrix (3X3) with entries thus: [1 2 3; 4 5 6; 7 8 9;] Circular shifts can be performed on any row or any column thus: row-(1/2/3)-(right/left) and column-(1/2/3)-(up/dn)...

Hi. I am a little stuck and I would appreciate some help. What is the acceleration due to gravity of the sun at the distance of 1.6 X 10^11 m? The asteroid revolves around the sun in 398 Earth days. 2. Homework Equations : F= (m*V^2)/r3. The Attempt at a Solution : First I found the...

1. A sound wave with frequency f = 2300Hz is sent into a circular tube of radius R=160cm through an opening at some point A. A receiver lies at point B, separated from A by an angle α=130°. The speed of sound in air is v=330 m/s. Sound propagates from A to B in both directions along the...

1. The Government in its "smart state" initiative wants a linear or circular accelerator for research and commercial use. Compile a recommendation on which one they should use. 2. No equations just need knowledge on Linear (Linac) and Circular (Synchotron) accelerators 3.The...

Homework Statement A massless spring of constant k is fixed on the left side of a level track. A block of mass m is pressed against the spring and compresses it a distance d, as shown in the figure. The block (initially at rest) is then released and travels toward a circular...

Consider an oblique circular cone of altitude h, base radius R, with apex directly above a point on the base circumference. What is the mean length (& variance) for the set of all rays from the apex to points on or within the base circumference?

In a cone circular line of 15 cm in height and radius 5 cm fits a body cylindrical topped by 1 hemisphere tangent to the base of the cone. Calculate the height and radius of Ia part cylindrical if the volume of the registered body is the largest possible Answer R = H = 3 cm V= pir^2h/3 cone...

Homework Statement Consider the Laplace’s equation, ∆u(r,θ) = 0, inside the quarter-circle of radius 2 (0 ≤ θ < π, 0 ≤ r ≤ 2), where the boundary θ is insulated, and u(r,\theta/2)=0 Show that the insulated boundary condition can mathematically be expressed as \frac{\partial u}{\partial...

Hey guys based on the Einstein train thought experiment we can say that different inertial frames disagree on simultaneity. In that specific example, the train observer is moving towards one thunder, and away from the second and in his frame the thunder in front of him occurs first followed...

Sorry if this has been asked a lot before but I did try a quick search for this but could find a simple answer. If I am at a fixed point on the equator and a friend is in a space station in a geostationary orbit, and ignoring GR, will their be time dilation between us? Or can we be...

Hi, does the intensity change when circularly polarised light passes through a linear polariser? I am thinking of a flow like this: natural light -> vertical linear polariser -> quarter wave plate -> horizontal linear polariser -> intensity? After the first polariser, the intensity is 50%...

Homework Statement A particle having charge q = 8.85 μC is placed on the axis of a circular ring of radius R = 30 cm. Distance of the particle from centre of the ring is a = 40 cm. Calculate electrical flux passing through the ring. Homework Equations Flux through a surface = ∫E.ds...

The following definitions are correct? We associate to a circular helix a complex numbers called complex torsion defined as follows: Definition: It's called complex torsion associated to a circular helix the complex number q=\tau+i\kappa , where \tau is the torsion of circular helix...

Let's imagine a rocket orbiting the earth. The rocket could be any real rocket with moderate speed, so that relativistic effects are not significant, and also rocket does not experice notable centrifugal or other acceleration (so the rockets reference frame would appear almost inertial). A...

Homework Statement A sphere on top of a table is attached to a rope which goes through a hole in the table and is attached to a bucket at the other end. The sphere moves in a uniform circular motion with radius R. Water is then added to the bucket and the radius for the sphere's circular...

Appreciated experts, I want to model the inflation of a thin and isotropic circular plastic membrane clamped by a ring. I need to determine the maximum deflection at the pole, stresses, strain, etc..., as a function of the applied pressure difference. The large deflection range complicates it...

For this question, I have to obtain a general quantization of motion in circular orbits by combining the equations (Where U(r) is potential energy): (mv2)/r= |(dU(r))/dr| With the angular momentum quantization of: mvr= nℏ Then use this to calculate the spectrum for circular motion in a...