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A number of balloons are attached to a circular disk with string. Some balloons are filled with air and some balloons are filled with helium. The disk is hung freely from ceiling of a room and is disk is rotated about its center. Assuming that the disk remains horizontal while rotating, describe what happens to the balloons?

(a) All the balloons move away from the center of the disk.

(b) All the balloons move towards the center of the disk.

(c) Air balloons move outwards away from the center and helium balloon move towards the center.

(d) Air balloons move inwards towards the center and helium balloon move out- wards the away from the center. I am in a doubt that is the centrifugal force will dominating and all balloon goes outside or some special effect(like pressure) will affect to helium balloon to go inside(like the behaviour of helium balloon in a car at a turn)

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Since the balloons are rotating, there must be a centripetal force that is keeping them going around the circle.

This resultant force is coming from a component of the tension in the string.

The centripetal force must point inwards towards the centre of rotation, so therefore the balloon must swing outwards so that part of the tension points inwards.

I can't see any difference in the behaviour between the helium and air balloons - in the helium balloons, the vertical component of the tension counters upthrust, whereas in the air balloons, the vertical component counters weight.


I made the following diagram to aid my explanation.

  • $T$ is the overall tension in the string.
  • $F_c$ is the centripetal force (resultant).
  • $F_b$ is what I am calling the "balancing force" - in the case of the air balloon, this is the opposite of the weight vector; for the helium balloon, it opposes the resultant upthrust (total thrust minus weight).

diagram

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  • $\begingroup$ What about wind resistance, which will be greater on the outer part of the balloons, pushing them inwards to where it is negligible in the center of rotation. $\endgroup$ – Adrian Howard Sep 16 at 21:15
  • $\begingroup$ @AdrianHoward Interesting though - I do not know enough about wind resistance to comment. $\endgroup$ – Joe Iddon Sep 17 at 19:03
  • $\begingroup$ I am no expert either it just seems that balloons are so light but bulky that wind force could overcome centrifugal force? $\endgroup$ – Adrian Howard Sep 17 at 21:54
  • $\begingroup$ @AdrianHoward The wind would provide an orthogonal force to the centrifugal force, so I think they would still hang out as I describe, but would "lag behind" the rotation of the disk. $\endgroup$ – Joe Iddon Sep 19 at 18:47

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