Understanding Centripetal Forces on a Rotating Bead Hoop

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Discussion Overview

The discussion revolves around the forces acting on a bead confined to a rotating circular hoop. Participants explore the dynamics of the bead in the context of Coriolis, centrifugal, and centripetal forces, as well as the reaction forces from the hoop. The scope includes theoretical considerations of forces in a rotating reference frame.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes the forces acting on the bead, including Coriolis, centrifugal, and centripetal forces, and questions the magnitude of the reaction force from the hoop.
  • Another participant suggests that the initial relative velocity of the bead is tangential and thus the initial Coriolis force is zero.
  • A participant expresses uncertainty about the original question and asks for clarification on the equations derived from the forces acting on the bead.
  • Further discussion includes the components of the reaction forces, with one participant questioning whether the radial component of the reaction force equals the centrifugal force component or if it must also account for centripetal force.
  • Participants agree that the reaction force must be perpendicular to the tangent of the hoop, including both vertical and radial components.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact relationship between the reaction force and the centrifugal force components, indicating that multiple views remain on how these forces interact in the context of the bead's motion.

Contextual Notes

Some assumptions regarding the frictionless nature of the hoop and the initial conditions of the bead's motion may not be fully articulated, leading to potential ambiguities in the analysis of forces.

Loro
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We have a bead confined on a circular hoop. The hoop is rotating around an axis tangential to it. Suppose the bead is intially at the point, farthest away from the axis, and has got some intial velocity.

I have a question - in the frame of the hoop, there is a Coriolis force perpendicular to the plane of the hoop, and a balancing reaction force. Then there is a centrifugal force, which has got a component normal to the hoop.

How big is the force from the hoop, balancing this one? Is it of the same magnitude as this normal component, or is it bigger so that it provides a net centripetal force associated with the motion of the bead around the hoop?
 
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Hi Loro! :smile:
Loro said:
We have a bead confined on a circular hoop. The hoop is rotating around an axis tangential to it. Suppose the bead is intially at the point, farthest away from the axis, and has got some intial velocity.

If I'm understanding it correctly, the initial relative velocity (which is tangential) is parallel to the axis of rotation, so the initial Coriolis force is zero. :confused:
 
Yes, that's what I mean. Sorry that I didn't make a picture.
 
I'm not sure what you're asking.

In the frame of the hoop, there's a centrifugal force away from the axis, there's a Coriolis force "vertically" out of the plane of the hoop, there's a centripetal acceleration towards the centre of the hoop, and there's a tangential acceleration …

when you put them all together, what equations did you get? :smile:
 
So if I were to compute the reaction forces of the hoop, there would be:

- one "vertically" out - balancing the Coriolis force
- and one towards the centre of the hoop

But would the latter be equal in magnitude to the component of the centrifugal force, normal to the loop? Or would it be that, + the centripetal force?
 
Loro said:
So if I were to compute the reaction forces of the hoop, there would be:

- one "vertically" out - balancing the Coriolis force
- and one towards the centre of the hoop

Yes, the reaction force (for a frictionless hoop) must be perpendicular to the tangent, so it will have a "vertical" component and a radial component.
But would the latter be equal in magnitude to the component of the centrifugal force, normal to the loop? Or would it be that, + the centripetal force?

Ftotal = ma …

Ftotal is the centrifugal force plus the reaction force

a is the centripetal acceleration plus the tangential acceleration

So, in the radial direction, the component of the centrifugal force plus the component of the reaction force must equal the centripetal acceleration times the mass.
 
Thanks, that answers my question! :)
 

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