Norton's Dome

[Macavity]

Can't find the *recent* link suggested by my Browser. But a FUN idea:
https://en.wikipedia.org/wiki/Norton's_dome

The "controversy" seems to have been around for quite a while though!
I have to admit, sometimes the idea of "spontaneous symmetry breaking"
in Particle Physics being... "inevitable" can seem a bit odd (to me) too? 😛

The original idea:  https://sites.pitt.edu/~jdnorton/Goodies/Dome/

[saac]

I've never seen that before, it's fascinating. I love the idea that a ball could sit at the apex for an indeterminate time and then spontaneously, without any external force, roll down the slope, all consistent with the equations of motion. Newton just got cool again  

Jim

[saac]

Wait a minute, just a further thought, how does that reconcile with conservation of momentum? Or have read into it incorrectly!

Jim 

[andrew s]

It's a very good example of idealised physics.  Another is Newtons cradle. 

If one just looks at the math you can have solutions in which any one of the balls  moves off after the initial impact if you restrict yourself to Newtons 3 laws.

You need to add something about rigidity of the balls etc. to get the classical result. 

15 minutes ago, saac said:

Wait a minute, just a further thought, how does that reconcile with conservation of momentum? Or have read into it incorrectly!

Jim 

I don't think it does as the tangential forces does work on the ball.

Regards Andrew 

PS on reflection there are many cases in physics where there are multiple solutions most of which are rejected as being un-physical even though they obey all the relevant laws and satisfy all the equations. 

 

Edited August 19, 2023 by andrew s

[saac]

Thanks Andrew, I need to spend some time on the maths later today and see if I can follow it through, I'm keen to properly get my head wrapped around this. Re the Newton cradle,  if you happen to have one handy (why wouldn't you) and super slo mo on your mobile phone it makes for a lovely video.  When you see it in slo mo it just begs the question "how do the balls know when to move and how many". It's a great way to spark curiosity and as an introduction to momentum.  

Jim 

[andrew s]

2 minutes ago, saac said:

"how do the balls know when to move and how many"

Yes, thinking deeply about simple cases is very insightful.  Try changing your frame of reference and have the s (normally)  stationary balls heading towards the the m (normally)  moving ones. Of course the kinetic energy and momentum in the two frames of reference are different. 

Regards Andrew 

[saac]

1 hour ago, andrew s said:

Yes, thinking deeply about simple cases is very insightful.  Try changing your frame of reference and have the s (normally)  stationary balls heading towards the the m (normally)  moving ones. Of course the kinetic energy and momentum in the two frames of reference are different. 

Regards Andrew 

It is so counterintuitive to accept that the natural state of an object is motion, that everything is born into a state of motion.  Doors seem to open once you wrap your head around it.

Jim