Circular Definition and 999 Threads

Homework Statement Explain why in circular motion there is a force pointing to the center of the trajectory. Use the momentum principle. Homework EquationsThe Attempt at a Solution So I choose two arbitrary points in the circular path and know that momentum and velocity are tangent to the...

Homework Statement An object, moving along the circumference of a circle with radius ##R##, is acted upon by a force of constant magnitude F. The force is directed at all times at a ## 30 \degrees ## angle with respect to the tangent to the circle. Determine the work done by this force when...

According to relativity, If magnetic field is just an electric field viewed from a different frame of reference, why is the magnetic field around the wire is circular?

Homework Statement A current carrying wire is bent into a circular loop with radius R and lies in the XY plane. A uniform magnetic field in the +z direction exists through out the plane of the loop. What is the magnetic force exerted on the loop? Homework Equations Fb = I lb sin (theta) The...

Hi there, I've come across the following question and drawn a free body diagram: A wedge with face inclined at an angle θ to the horizontal is fixed to a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is...

Homework Statement Attached. Homework Equations The Attempt at a Solution Hi. This question has me really puzzled; I simply don't know where to start with this one and thus am not sure of any relevant equations. It seems to be a problem about small perturbations to the circular...

Homework Statement A thin circular ring of radius R has charge Q/2 uniformly distributed on the top half, and -Q/2 on the bottom half. a) What is the value of the electric potential at a point a distance x along the axis through the center of the circle? b) What can you say about the electric...

Hi, I have a data vector that consists of directions measured in an experiment. I wish to create a probability density function. As the data is circular and multimodal I use a kernel density estimate with von Mises distribution (essentially a Gaussian on the unit circle) as the basis function. I...

I am trying to get used to using a Data Physics analyzer at work in order to measure the natural frequency of components of a larger project I am involved in, my method described is intentionally crude as I was trying to do this as a quick play around before diving into the real thing.. To...

I am self studying Kleppner and Kolenkow's an Introduction to mechanics. But i have one doubt about how they got into the equation no 3 of the example problem 9.3 in Central Force Motion. Please clarify my doubt.

Hi Guys, new poster here. I am currently doing a practical report on Uniform Circular Motion, where we had to swing a rubber stopper around attached to a length of string and mass. I have to do a write up, including the background theory. I have searched everywhere but I have found no clear...

Homework Statement A roller-coaster car speeds down a hill pas point A and then rolls up a hill past point B. A. Car speed = 20 m/s at point A. If the track exerts a normal force on the car of 2.06x10^4N at this point, what is the mass of the car? (account for gravitational force) B. What is...

Hey all, I'm stuck on this problem and not sure how to proceed/if I'm in the right direction. Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below (A) find the direction...

In the pulley system shown in Figure Q1 the tangential forces on the pulleys are shown. Each pulley adds an additional load / weight of 500N on the shaft. Calculate a suitable shaft diameter so that to avoid failure by the maximum shear stress criterion. The tensile yield strength of the shaft...

Homework Statement Purely a conceptual/ terminology question, a simple yes or no will suffice :) In circular motion, will a point on its circumference will have a LINEAR acceleration which can be broken into two components- the RADIAL component which is v2/r and the TANGENTIAL component which...

When making an extension from linear dipole antennas to small circular antennas, I am only coming across expressions for a magnetic dipole moment (as opposed to having just an electric dipole moment for a linear dipole antenna). The expression being: m = πr2I at its peak The above expression...

This was a homework problem; after five tries, I still did not get it, and I can't figure out how to get at the answer the assignment gave me. I could not find the answer anywhere that didn't get into angular velocity, which we are not at yet (and also did not give me the answer!). 1. Problem...

Homework Statement A pendulum with a bob on the end is attached to a stand. The stand has a rod sticking out such that when the string of the pendulum strikes it, it starts to undergo circular motion. Consider the bob being released from a height such that when it strikes the rod, it only just...

Homework Statement Q.1. Explain the changes in the tension of a piece of string which is being swung vertically with a bucket of water at the end. What would the minimum centripetal acceleration need to be for water to not fall out?Homework Equations ac = v^2/r The Attempt at a Solution The...

Homework Statement [/B] We are given a graph, with the information of the period, and the radius of the string. We amassed this data on our own. The graphing of it is quartic, but we have to make it into a linear graph?Homework Equations N/A The Attempt at a Solution [/B] First we tried to...

Homework Statement A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/h to 50 km/h in the 15 s that it takes to round the bend. The radius of the curve is 150 m. Compute the total acceleration at the moment the train speed reaches 50 km/h Homework Equations a =...

Suppose a particle undergoing uniform circular motion completes a cycle, then ##<\vec{v}> = \frac{Δ\vec{r}}{Δt} = \vec{0}##. But then again, isn't it also the mean of the two velocity vectors at that point? And aren't those two velocity vectors equal? So if the velocity at that point were, say...

Homework Statement [/B] If the speed was doubled, what would the radius and period be to keep the same acceleration? Homework Equations a = v^2/R T = 2piR/tThe Attempt at a Solution So with my understanding it is as follows: (2v)^2/R This makes it 4v^2/x = a since a=v^2/R Setting this into...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution [/B] Honestly, I don't even know how to begin this problem. I've drawn myself some free body diagrams, but I'm uncertain of all of them. The weight of the bar is just (0,-mg) at .9r from the pivot point. But I don't know how...

In the picture, at point 2 (the bottom of the ramp) the normal force of the object has a greater magnitude than weight. I understand that the normal force has to be greater than the weight since the acceleration points towards the center of the circle and the net force is in the same direction...

I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...

Hi, I have previously made a post in order to gain some insight in my rather out of control project. Long story short I am investigating vibration of a circular plate and its standing waves. After consultation at this forum I have been guided in the direction of acoustics and bessel functions...

Homework Statement Calculate the average vector velocity between 0 and pi/4 sec. Homework Equations x=rcos2t y=rsin2t Vx=2rsin(2t) Vy=2rcos2t Ax=4rcos(2t) Ay=-4cos(2t) Circular path is x^2+y^2+r^2 The Attempt at a Solution I'm not sure if I am missing something simple or not, What I need to...

Homework Statement Evaluate the matrix elements ## {\mathbb S}=\left( \begin{array}{cc} \langle x|\mathbb{\hat J}_z|x\rangle& \langle x|\mathbb{\hat J}_z|y\rangle\\ \langle y|\mathbb{\hat J}_z|x\rangle &\langle y|\mathbb{\hat J}_z|y\rangle\end{array}\right)## by expressing the linear...

Homework Statement (a) Find the proper time in the rest frame of particle (b) Find the proper time in the laboratory frame (c) Find the proper time in a photon that travels from A to B in time P Homework EquationsThe Attempt at a Solution Part(a) [/B] The metric is given by: ds^2 =...

Homework Statement A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion.(Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total...

Homework Statement http://www.sumoware.com/images/temp/xzmomoeqpspoqxcq.png A block with mass m is static at first at the height of 2R (see picture above) and then slides without friction. a) Determine where the block leaves the track b) Determine the maximum height which the block reaches...

Homework Statement A ball with the mass m is attached to a rod, suspended by two strings both with lengths L. The rod is rotating with the angular velocity ω and the ball rotates with it in such a way that the strings are taut and the ball moves in a circular pattern. I tried to draw it on my...

√Homework Statement Show that the gravitational field due to thin uniform circular plate of radius a at point distant R from center and on the axis passing through the center and perpendicular to the plane of the plate is given by E= -2πGρ[1-R/(a^2+R^2)^1/2] Homework Equations F= GMm/r^2...

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket...

Hi, Could you explain the reason why the velocity varies in the wake region behind the cylinder in "flow over a circular cylinder"? the velocity variation is, minimum at a point parallel to the centre point of the cylinder and increases to free stream velocity as the vertical distance increases...

Homework Statement A circular coil with center on the z axis and orthogonal to the xy axis carries a current. The coil is in a magnetic field B with axial symmetry compared to the x axis. B forms an angle θ with the z axis. Calculate the magnetic force acting on the coil. 2. Homework...

Homework Statement object of mass 0.20 kg tied to a string is made to move in a vertical circle. When the object is at the highest point, the tension in the string is zero. Determine the tension in the string when the object is at the lowest point. [11.8 N] Homework EquationsThe Attempt at a...

Hi all, I had a question that I can't seem to find an answer too. I was hoping people could point me in the right direction, or let me know if there is an "easy" method. It has to do with the classic example of two stones in water producing constructive and destructive interference...

Homework Statement For low-speed(laminar) , steady flow through a circular pipe, the velocity u varies with radius and takes what form? Please see this link for picture of the pipe...

Homework Statement A .8 kg lead ball is whirled on the end of a string 5 meters long. When the ball passes through point A at the top of the path, the tension in the string is 4.96 N. What is the speed of the bob at point A? *NOTE - POINT A is at the top of the circle... Homework Equations...

Homework Statement Bob starts at rest from the top of a frictionless ramp. At the bottom of the ramp, he enters a frictionless circular loop. The total mass of the child and the cart he sits in his m. What must the height of the ramp be in order for the cart to successfully traverse the loop...

1. A conducting loop is shrinking in a constant ##\vec{B}##-field that is perpendicular to the loop-axis. The radius of the loop is given by ##r(t)=r_{0}e^{-at}##. The resistance in the loop is ##R(t)=2 \pi \rho r(t)##. What force is needed to keep the loop shrinking like this?2. Faraday's law...

Homework Statement In a classical model of a multi-electron atom, electrons are assumed to move in a modified electrostatic potential $V(r)$, given by; $$V(r)=\dfrac{-k}{r}e^{-r/a}$$ Show that the effective potential is ; $$V_e(r)=\dfrac{J^2}{2mr^2}+\dfrac{-k}{r}e^{-r/a}$$ Then show that...

Homework Statement When you are spinning an object in a circular path, you are applying centripetal force towards the center of the circle while the velocity vector is perpendicular to it. Therefore the Force component affecting the velocity is FCos(90) = 0. Keeping this in mind, how can you...

My book says that for uniform rotational flow, the velocity at any point is proportional to r (v = wr.) In vortex flow, the velocity at any point is proportional to 1/r (angular momentum is conserved.) However, in uniform rotational flow, isn't angular momentum also conserved so the same logic...

Homework Statement A 1 kg ball with a radius of 20 cm rolls down a 5 m high inclined plane. Its speed at the bottom is 8 m/s. How many revolutions per second is the ball making when at the bottom of the plane? Homework Equations circumference = 2πr velocity = distance / time = circumference /...

Homework Statement A spaceship in outerspace has a donut shaped with a 500 m outer radius. The inhabitants stand with their heads towards the center and their feet on an outside rim. Over what time interval with the spaceship have to complete one rotation on its axis to make a bathroom scale...

This is the equation for the cone A \sqrt{x^2 + y^2} The double integral \iint A \sqrt{x^2 + y^2} \space dy \space dx \space \space \space\text {From x= -1 to 1 and y=} -\sqrt{1-x^2} \space to \space \sqrt{1-x^2} \text{ is very difficult to evaluate. I've tried polar coordinate substitution...

I don't understand, how can tidal forces make the orbits more circular? Perhaps it has something to do with the fact that in elliptical orbits (unlike in circular orbits) the velocity is not always perpendicular to the acceleration? Or maybe it does not have to do with the tidal forces from the...