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newtonian mechanics - Motion of bead on a rod - Physics Stack ...

Consider a coordinate system x y on the plane of the rotating rod and fixed in an inertial frame, with the rod's pivot at ( 0, 0). The position of the bead can be written as. r ( t) ( cos. ⁡. ω t, sin. ⁡. ω t), where r ( t) is the distance from the pivot and we're assuming that the rod is on the x axis at t = 0.

Rotating Bead Rod V Rod - Image Results

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Bead on a rotating rod | Physics Forums

In the frame fixed to the rotating rod, the force acting on the bead is radially outwards and is of magnitude ##m\omega^2r##. Hence, $$m\frac{d^2r}{dt^2}=m\omega^2r$$ The solution to the above equation is: $$r(t)=Ae^{\omega t}+Be^{-\omega t}$$ The motion presented in the question is possible when ##r(0)=r_0## and ##r'(0)=r_0##. Is this correct?

Bead on rotating rod | Physics Forums

The rod rotates in a plane about one end at a constant angular velocity w. Show that the motion is given by r=Ae^(-γt)+Be^(γt), where γ is a constant which you must find and A and B are arbitrary constants.

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Bead on a Rotating wire - (Lagrangian Mechanics) - YouTube

A particle of mass m is free to slide on a thin rod / wire. This wire rotates in a plane about an end at constant angular velocity. Obtain the solution of mo...

Phys 325: Midterm #1

The rod is rotating around the z-axis at constant angular speed ⌦ and the angle is constant. A bead of mass m is on this uniformly rotating rod, and the bead is constrained to stay on the rod but is free to move along the rod in a frictionless way. The bead is initially placed at rest a distance r from the point at which the rod is attached to the z-axis.

A bead is constrained to slide along a frictionless rod of l...

A bead is constrained to slide along a frictionless rod of length L. The rod is rotating in a vertical plane with a constant angular velocity about a pivot P fixed at the midpoint of the rod, but the design of the pivot allows the bead to move along the entire length of the rod. Let r (t) denote the position of the bead relative to this rotating coordinate system as shown in Figure 5.R.2.

A bead slidding on a rotating rod - YouTube

Physics problem on Friction & rotation:A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A...

Steady states of non-axial dipolar rods driven by rotating fields

m of rod b with the ce nter of bead j of rod a (see Fig 1). The force on bead m due to b ead j is given by: ... ternal rotating magnetic field, resulting in an effective.

PHY5210 W08 Lecture 5 - Wayne State University

ma'= Freal- mΩ[dot] × r'- 2mΩ× v'- mΩ× (Ω× r') Example: Bead on a Rod. A smooth rod of length l rotates in a plane with a constant angular velocity Ωabout an axis fixed at the end of the rod and perpendicular to the plane of rotation. A bead of mass m can slide along the rod without friction is initially positioned at the stationary end of the rod and given a slight push such that its initial speed directed down the rod is ε = Ωl (draw figure).

lecture 7 - sites.fas.harvard.edu

related to the motion of the bead along the rod, and the second one with the rotation of the rod. Because these two motions are perpendicular, there is no cross term and the total kinetic energy is just a sum of the two effects. In this case, there is no potential, so the Lagrangian is just given by the kinetic energy, (18),