2 questions regarding physics.

[unbiased]

Dear Friends, I feel a little baffled by the following. Will somebody help please.

1. Space is homogenious and isotropic. This is reflected in the law of conservation of linear momentum and conservation of angular momentum. How?

2. Time is also homogenious and isotropic. Homogenity is reflected inn the law of conservatiion of energy. (How?). Nobody is sure what is the physical manifestation of
isotropic property of time.

Thanks in adv.

 

[Calin]

Let's assume space would not be isotropic (it would not have the same properties in every direction). This means by example that distance would be smaller along a movement axis, and larger around an axis perpendicular on it.
Now, a circular motion in the plan determined by these directions will have... what? If you say constant angular velocity, its linear velocity would change along its trajectory. Also, its radius of movement would change.
Calin

 

[silverpig]

I don't have time now, but google for an explanation on how conservations laws <--> symmetries.

 

[Mday]

pfft

If you're going to ask for help on homework, just say so.

 

[iwantanewcomputer]

i think isotropic here means that heat or energy is not transported in or out of space/time...another way of sayig the law of conservation of energy? homogenious time/space doesn't seem to make sense unless you are still talking about the universe's energy being constant. i would just take that to mean time does not change from one point of view to the next, which it does according to relativity

 

[BitByBit]

Well, I find this question a little vague, but it can nonetheless be expressed.

1: If space is homogeneous and isotropic, then the distance between any two points will remain unchanged anywhere in the universe.
So, in the case of linear momentum, we have:

p = mv or alternatively:
p = m(ds/dt).

ds/dt, or the change in distance with respect to time is of course dependent on the above assumption.
If ds changes while dt remains constant, then so does the value of ds/dt, or velocity.
In that case, mv is not conserved.

Angular momentum deals with the momentum of an object in circular momention for varying values of r.

Angular velocity in rad/s is given by: d(theta)/dt, or v/r.
The linear velocity of an object in circular motion is the angular velocity multiplied by the radius:

v = r.v/r

Angular momentum is therefore given by:

p = mr.v/r = mv

If we change the value of r while keeping the value of v/r constant, we must compensate with increasing the linear velocity.
So if we halve r while keeping the momentum constant, we get:

p = m(r/2).(2v/r) = mv

When reducing the radius, we also expect the distance travelled by the object (the perimeter) to change accordingly.
So, if we halve the radius, the value of r(theta) should also halve.
If this is not the case, then angular momentum is not conserved.

2: The only way I can see to marry these concepts is that velocity is a function of time, and Kinetic Energy is a function of velocity (E = (1/2)mv^2).
When dealing with collisions (as the conservation laws were intended to be used), we end up with: Energy before collision = Energy after collision.
Momentum is conserved in collisions, but KE is not, since no collision is completely elastic, and some energy ends up being converted into other forms.
It is difficult however, to see where time comes into this.
If we are talking about the transfer of energy from one object to another, then that transfer must occur over a period of time, no matter how brief, given by the equation of power: P = E/t.
Changing the value of t would simply mean in this case that it energy transfer takes a different amount of time to occur, but that doesn't imply that the total amount of energy transferred will be changed.

I'm sure there's someone on this forum who can provide more insight here.