A spinning wheel

by andywelik
Tags: spinning, wheel
Baluncore is offline
Feb12-14, 02:54 PM
P: 1,278
Define a circle with radius r, centred at the origin, x^2 + y^2 = r^2
The centre is specified as a point, P(x,y), where x = 0 and y = 0.
Rotate that circle continuously about it's centre.

The x and y coordinates of the centre do not change with that rotation.
Therefore the point at the centre is not moving.

In mathematics, a point does not have an orientation.
AlephZero is offline
Feb12-14, 03:06 PM
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Quote Quote by Baluncore View Post
In mathematics, a point does not have an orientation.
This is rather missing the point (groan!). If we are talking about classical mechanics of a solid, by any reasonable definition of the shear strain at the axis of rotation, the "center point" does "rotate".

The mathematical reason is that strain is not a property of an isolated point of material, it is also property of the the material close to that point.

And if we are talking about quantum mechanics, a question about "a particle in the center of the wheel" is rather meaningless.
Baluncore is offline
Feb12-14, 04:05 PM
P: 1,278
The question becomes one of the difference in definition of a particle and a point. As you zoom in closer, does the particle at the centre ever become a mathematical point at the centre. I believe a particle always has orientation while a mathematical point never does. Also, a particle always has a mass, a point never has a mass.

At some molecular scale the physics of shear as a bulk property will cease to be valid. It will be replaced by a space frame of directional bonds. That space frame and each part of it, is also a directed particle.

No matter how closely you zoom in, a physical particle will always be a particle with an orientation and mass. It can never become a mathematical point without orientation or mass.
andywelik is offline
Feb13-14, 06:33 AM
P: 10
Quote Quote by Nugatory View Post
No, because there will still be a single point at the center of the enlargement, and we can ask the same question about that point. And we can repeat this process (in our imagination) forever without ever getting to an end.

There was much sense in CWatters response earlier in this thread: "Funny things happen when you look at infinity or 1/infinity"; you are basically talking about 1/infinity when you try narrowing down to a single point.
You are right. Thanks, Infinity has no beginning nor end.

Now I realize that no one should think about a dead-centre point when it comes to a spinning/rotating disc/wheel. Even though the linear speed is zero at the dead centre, logically thinking, zero speed is never reached in angular speed, no matter how much one enlarges the dead-centre point.

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