A question about bicycle

[khaled]

I was reading articles, when I came upon this "riding a bicycle is safe." from an article on Noether's theorem,

 

What I don't understand, is how was that riding a bicycle is safe concluded, and what is Noether's theorem ?

[MigL]

Noether's theorem states essentially that any symmetry leads directly to a conserved quantity. A thorough explanation/discussion is easily found on Wiki.

Some examples...

time => mass/energy

translational => momentum

rotational => angular momentum

 

Those are the simple ones, but various gauge symmetries lead to other conserved quantities such as charge. and others.

 

I'm at a loss to explain the connection to a bicycle, unless it pertains to angular momentum and associated increase in stability. Maybe if you post a link to the article in question ... ?

Edited March 27, 2012 by MigL

[khaled]

"If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric

translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see

it’s angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move." NY Times

 

Someone who's studying Engineering told me that the moving thin wheels are tangling ground by a continuous line,

unlike not-moving thin wheels that are not moving, they are tangling ground by a point

 

The last quote I understand well, but don't understand the meaning behind it is "whether you throw a ball in the air tomorrow

or make the same toss next week will have no effect on the ball’s trajectory" NY Times

 

The article conclusion is that Noether’s theorem shows that a symmetry of time is directly related to the conservation of energy.

 

I know what is the conservation law of energy, but what is the symmetry of time .. I know super symmetry theory that says

that universe is made of matters and anti-matters that sum up to Zero.

Edited March 27, 2012 by khaled