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I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not given. Any suggestions?

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Our goal here is an answer conceptual questions as opposed to homework questions, so I would prefer omitting the picture and asking something like, "Suppose I have a small bit of mass stuck on the outside of a spinning hoop. I know by intuition that the hoop is essentially 'trying to throw the mass off', but I don't know how to calculate this effect. How would I find the force between the hoop and the mass?" – Mark Eichenlaub Nov 7 '10 at 23:51

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I'm not sure I totally understand the question, but I can make an educated guess. Firstly, I envisage a person sitting on the merry-go round with their body pointed tangentially to the circle, in which cases no force in that direction is required.

However, if the person is free to move radially (can slip inwards/outwards), then a force is required to counteract the centripetal force. In other words,

$$F_{holding} = F_{centripetal}$$

Consider the appropriate equation for centripetal force in terms of your known variables, and you can then plug in the values to get the answer.

(P.S. Don't look at my edit unless you want the answer, best you try yourself first!)

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Question in English: what is the name of a radial force acting toward the center ? What is the name of the pseudo-force introduced in the rotating frame of reference ? Because you said "to counteract the centripetal force" ... I would say that the force we are talking about is the centripetal force... (in French we make a distinction "centripeDe" and "centripeTe"). – Cedric H. Nov 7 '10 at 22:33
Yes this was it, thanks! – maq Nov 7 '10 at 22:39
@fprime: Glad to help. This is a pretty good example of a homework question; I see too many bad ones. :) – Noldorin Nov 7 '10 at 22:41
@Cedric: Yes, this is a slight problem of language. I'm considering the whole problem from the inertial frame of the ground. In this case, there is only a centripetal force. A force needs to be exerted by the person to counteract this, otherwise the person would fly off. Of course, you can also consider the problem from the rotating reference frame and talk about the centrifugal pseudo-force. Just complicates things though, in my view. (Oh, and in English centripedal is not a word - maybe a common mispelling of centripetal. Confusing, if you speak French, I admit!) – Noldorin Nov 7 '10 at 22:45
OK thanks for this clarification ! So centripetal and centrifugal. – Cedric H. Nov 7 '10 at 22:46
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Think about these:

  1. What is the shape of the path the person takes?
  2. What force is needed to keep the person traveling along that path?
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