Understanding Centripetal Forces on a Rotating Bead Hoop

In summary, the centrifugal force on a bead rotating around a circular hoop is balanced by a reaction force that is perpendicular to the hoop and has a normal component.
  • #1
Loro
80
1
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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  • #2
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:
 
  • #3
Yes, that's what I mean. Sorry that I didn't make a picture.
 
  • #4
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:
 
  • #5
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?
 
  • #6
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.
 
  • #7
Thanks, that answers my question! :)
 

What is a centripetal force?

A centripetal force is a force that acts towards the center of a circular path and keeps an object moving along that path. It is required for any object to move in a circular motion.

How is centripetal force related to the motion of a rotating bead hoop?

The centripetal force on a rotating bead hoop is what keeps the beads moving in a circular path. Without this force, the beads would move in a straight line tangent to the hoop's circumference.

What factors affect the strength of the centripetal force on a rotating bead hoop?

The strength of the centripetal force on a rotating bead hoop is affected by the speed of rotation, the mass of the beads, and the radius of the hoop. The larger the speed or mass, and the smaller the radius, the stronger the centripetal force will be.

How can the centripetal force on a rotating bead hoop be calculated?

The centripetal force can be calculated using the formula Fc = mv²/r, where Fc is the centripetal force, m is the mass of the beads, v is the speed of rotation, and r is the radius of the hoop.

What are some real-life examples of centripetal force on a rotating bead hoop?

A ferris wheel, a spinning top, and a planet orbiting around the sun are all examples of objects where centripetal force is at play. The centripetal force is responsible for keeping these objects in their circular paths.

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