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# M2 vertical circle problem

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1. M2 vertical circle problem
I really don't get vertical circles. e.g question 7 of this paper

http://store.aqa.org.uk/qual/gceasa/...W-QP-JUN08.PDF

I just don't understand the answer for 7a and 7b on this mark scheme

http://store.aqa.org.uk/qual/gceasa/...W-MS-JUN08.PDF

why does the answer for 7a say : "At top, for complete revolutions: (mv)^2/a = mg"

And why is it that for 7b, the answer says "at C, speed of particle is (3ag)^(1/2)"

It would be great if anyone could help. Sorry if the question is worded confusingly.

Thank you
2. Re: M2 vertical circle problem
Hi, it doesn't quite say that but rather mv^2 / a = mg, mg is the force acting vertically downwards due to gravity and mv^2 / a is the centrifugal force acting vertically upwards (in the case where it's at the top of the rotation) as a result of the rotation. If the string is to not be slack we require that the force up is greater than or equal to the force down, so we consider the equality case.

As for 7b you can find the speed at C by conservation of energy.
3. Re: M2 vertical circle problem
(Original post by Allofthem)
Hi, it doesn't quite say that but rather mv^2 / a = mg, mg is the force acting vertically downwards due to gravity and mv^2 / a is the centrifugal force acting vertically upwards (in the case where it's at the top of the rotation) as a result of the rotation. If the string is to not be slack we require that the force up is greater than or equal to the force down, so we consider the equality case.

As for 7b you can find the speed at C by conservation of energy.
Thanks for your help. But I've always been taught that the centripetal force always acts towards the centre of the circle, is that wrong then?
4. Re: M2 vertical circle problem
(Original post by withoutwax1111)
Thanks for your help. But I've always been taught that the centripetal force always acts towards the centre of the circle, is that wrong then?
No, it's not wrong. Nothing Allofthem has said contradicts that.

Centripetal towards the centre of the circle.
Centrifugal away from the centre.

More can be said on the nature of the centrifugal force, but I'll leave that to wiki.

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Last updated: June 15, 2012
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