# What is Bead: Definition and 133 Discussions

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1. ### I Hamiltonian of the bead rotating on a horizontal stick

Hi, In David Morin's "Introduction to classical mechanics", Problem 6.8, when deriving Hamiltonian of the bead rotating on a horizontal stick with constant angular speed, the Lagrangian derivative over angular speed isn't included. Why is that? Specifically, the Lagrangian takes form...
2. ### I Bead on a vertical frictionless ring

A bead is kept at the bottom of a vertical frictionless ring , if the ring is given an acceleration a horizontally, what is the maximum angular displacement of the particle? The problem is easily solved from the frame of reference of the moving ring, I am however Intrested in a solution without...
3. ### Circular Motion - Newton's Second Law: Bead on a Rotating Hoop

For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...
4. ### Oscillation of bead with gravitating masses

The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...
5. ### Frequency of Oscillations of a Bead Resting on a Gas

Hi, this is a question from my textbook that I can't quite make sense of. I don't really know where even to begin, to be honest. The only thing I can think of is that the bead is at equilibrium, thus the force of gravity is equal to the pressure exerted by the gas. I don't know where the heat...
6. ### Centripetal Motion problem -- A bead sliding around a horizontal loop

To be honest I am a bit clueless first with how to interrupt this question I think the bead is going around a wall type thing where there is friction both in the up and X direction. Some hint to get some ideas running would be great
7. ### Bead sliding on a Vertical Circular Loop versus in Free Fall

I can evaluate the first beads motion easily A to B is -2Rj considering the point B as y=0 the motion of the bead will be -gt^2/2+2R=0 which implies t=2√(R/G) , this is ok but what I am struggling with is A to C I can see that the angle between the beads weight and it's negative normal force...
8. ### Bead sliding on a uniformly rotating wire

Hi I am working through some notes and came across this example. The wire rotates at angular frequency ω so the polar angle is given by θ = ωt. The generalised coordinate is r. Using the Euler-Lagrange equation leads to d2r/dt2 = rω2 The notes then state that this leads to the solution r = Aeωt...
9. ### Applying D'Alembert's principle to a bead on an elliptical hoop

Hi I've written D'Alembert's principle as you can see in the attached files. I computed the virtual work done by the weight and the elastic force (since the work done by the normal force is zero) and then I used the fundamental hypothesis, which states that the constraint forces can be written...
10. ### Bead on a rotating stick and the Lagrangian

A stick is pivoted at the origin and is arranged to swing around in a horizontal plane at constant angular speed ω. A bead of mass m slides frictionlessly along the stick. Let r be the radial position of the bead. Find the conserved quantity E given in Eq. (6.52). Explain why this quantity is...
11. A

### Small bead - Circular loop Problem

Homework Statement: A small bead is fixed on a circular loop of radius R as shown in the figure below. The loop is rotating about YY axis with constant angular acceleration ‘α’. The loop starts from rest, then, the bead is in circular motion, then acceleration of the bead at instant ‘t’...
12. ### Find the time at which the bead will start slipping

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance ## L ## from one end A of the rod.The rod starts from rest in angular motion about A with a constant angular acceleration ##\alpha## .If the coefficient of friction between the rod and the...
13. ### Find Serret-Frenet Triad for Curve y = f(x): Solve Diff. Eq. -U`(s)

For the case first case U=x^2/2 : 1) Find the Serret-Frenet Triad for a any curve y = f(x): For a curve on a plane, the Triad could be find in this way: 2) The vector force resultant acting in the bead could be discribed in this way: 3) The vector force acting in the bead could be discribed...
14. ### Solving for the tangential force for a bead on a wire

Homework Statement Homework EquationsThe Attempt at a Solution I am pretty sure that I solved part a correctly. However, I feel as though my solutions for parts b and c are not quite correct because they seem simple. For instance, my solution for part b argues that the tangential force is...
15. ### Physical representation of bead sort

Bead sort is a not practical sorting algorithm that suppose to have a time complexity of ##O(\sqrt{n})##in the real world. I thought it would be great if a device that can take numbers from the computer,then turn it into analog stuff that the device can read,drop the beads,and return it...
16. ### Which powers works on bead on a string?

Homework Statement I know that a bead is threaded on an metal sring (no T), and the bead is not moving/ The metal string moves in circular motion at a slope of 60 degrees. The string moves one spin in one second/ which powers works on the bead? Homework EquationsThe Attempt at a Solution

39. ### When does the bead fly off the rod?

Homework Statement A rod of length L is fixed at one end, and rotates in the X-Y plane with angular velocity ω. (To be clear, it is sweeping out an area of ##π (L/2)^{2}##.) A bead starts at position ##r(0)=L/2## with ##\dot{r}(0)=0##. Find ##r(t)## and the time it takes for the bead to fly...
40. ### Bead on a wire in a cart

Homework Statement The bead of mass m starts to slide without friction from point A. the mass of the cart and the rail is M. What is the max displacement of the wagon during the motion of the bead? What is the force the rail exerts on the cart when the cart's velocity is maximum? What is the...
41. ### Calculate flux in a ferrite bead on a wire

Suppose that a ferrite bead is put around a cable where a constant current I flows, just like in this image. The coordinate system has the z axis along the cable. Let's evaluate the current through the (x,y) plane: according to the Ampère's law, the only magnetic field component generated by...
42. ### MHB Is Two-Colour Bead Necklace Arrangement Possible?

Hello! (Wave) We have a necklace with $64$ beads from $8$ different colours. Is it possible that they are put in such a way that if we go along the necklace in one direction (in any of the two) then we see all the possible successions of two colours exactly once?
43. ### Lagrangian: Bead on a rotating hoop with mass

Homework Statement 'Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop is free to rotate about the vertical axis. Determine all relative equilibria of the bead.'...
44. ### Angle of rotation of a bead embedded in a support

Hello Everyone, I want to explain my problem. I am quite starter in Ansys... I have modeled a simple bead embedded in a support as you will see in the screenshot. Then I apply a torque onto the bead to make it rotate a bit. I want then to calculate the angle of rotation the bead I have made...
45. ### Normal force of a bead moving around a horizontal ring

A bead of mass m is threaded on a metal hoop of radius R. There is a coefficient of kinetic friction µk between the bead and the hoop. It is given a push to start it sliding around the hoop with initial speed v0 . The hoop is located on the space station, so you can ignore gravity Find the...
46. ### Bead attracted by spheres

Homework Statement A bead of mass m slides without friction on a smooth rod along the x axis. The rod is equidistant between two spheres of mass M. The spheres are located at x = 0, y = ± a, and attract the bead gravitationally. (a) Find the potential energy of the bead. (b) The bead is...
47. ### Power required to move a glass bead in a viscous fluid

Homework Statement A bead of radius R(=5 μm) is trapped by an optical beam and moved through a viscous fluid at a speed vd of 20 μms-1. If the viscous drag is given by Stokes law: F_{d}=6\pi \eta Rv_{d} obtain an expression for the laser power (intensity). If the process only has an...
48. ### Bead sliding on a rotating rod

Bead is at rest on a thin rod pivoted at one end. Bead is about a cm from the pivoted end of the rod. Rod now starts rotating with an uniform angular velocity w rad/sec. 1.What curve does the bead trace from the point of view of an inertial observer? Here what i think... solution of the...
49. ### Rotational Physics - Bead on spinning ring

I think I'm not understanding some conceptual part of rotational kinematics because all the questions seem connected. I want to figure it out as best I can so please don't solve it but any hints in the right direction would be really appreciated, thanks! The Question: A stiff piece of wire is...
50. ### Single bead on a vertical circle.

Imagine that a single bead has a hole in it. It is passed inside a " vertical " circle with no friction. Imagine that the "vertical"circle moves by spinning around its vertical axis and that the bead is, AT THE BEGINNING, on the bottom of the vertical circle. We had another problem related to...