# Math Help - Vertical Circle ..Bead on a wire problem?

1. ## Vertical Circle ..Bead on a wire problem?

At a general point ( say at angle theta above the horizontal) on a vertical circle, how do you know whether the reaction force is point inwards and contributing positively towards the net force towards the centre or whether the reaction force is directed outwards?

For example, when looking at a particle on a string we always draw the tension towards the centre but which way is the reaction force with a bead on a wire?

2. ## Re: Vertical Circle ..Bead on a wire problem?

Originally Posted by rodders
At a general point ( say at angle theta above the horizontal) on a vertical circle, how do you know whether the reaction force is point inwards and contributing positively towards the net force towards the centre or whether the reaction force is directed outwards?

For example, when looking at a particle on a string we always draw the tension towards the centre but which way is the reaction force with a bead on a wire?
The direction of the reaction force depends on the speed that the bead is moving. For instance, if the bead is moving fast enough, the reaction force of the wire on the bead is inward.

for $\theta$ equal to the bead's angular position above to the horizontal ...

$F_c = \frac{mv^2}{r} = mg\sin{\theta} + N$

where $N$ is the magnitude of the reaction force in the radial direction.

As the bead slows from the speed in the above equation, $N$ decreases to 0. The speed where this occurs is ...

$v = \sqrt{rg\sin{\theta}}$

Slower still, and the reaction force is directed outward ...

$F_c = \frac{mv^2}{r} = mg\sin{\theta} - N$

3. ## Re: Vertical Circle ..Bead on a wire problem?

Interesting thanks... felt it was something like this. So in general take it outwards?
And is this a case of the bead sitting on the wire or vice versa?

4. ## Re: Vertical Circle ..Bead on a wire problem?

Originally Posted by rodders
Interesting thanks... felt it was something like this. So in general take it outwards?
No ... as I said, it depends on the speed of the bead.

5. ## Re: Vertical Circle ..Bead on a wire problem?

And what is actually going on?
Is the bead sitting on the wire in one case and bead being pushed out in the other?

6. ## Re: Vertical Circle ..Bead on a wire problem?

yes ... it's all tied to the dynamics of centripetal force.