Speed of Point on Expanding Sphere

In summary: If you take a ball and throw it in a certain way, it will follow a certain parabolic path. If you then take that same ball and throw it in a different way, it will follow a different parabolic path. This is not physics or mathematics, but merely your decision to throw it in a different way.So the question is not answerable as it stands.Summary: The tangential velocity of an object moving across the expanding surface of an expanding sphere is dependent on the initial conditions of the object's motion and cannot be determined by physics or mathematics alone. Clarification of the setup is needed to answer the question.
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TL;DR Summary
Suppose we have an expanding sphere. That means that the surface ##4 \Pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b r##. Does this limit the speed at which a point can move on the surface?

Reference: https://www.physicsforums.com/forums/special-and-general-relativity.70/post-thread
Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?
 
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  • #2
Limit in what way? In SR the speed of a particle as measured in an IRF is limited by ##c##. Having an expanding physical object, if that is what you mean, doesn't change that.
 
  • #3
PS the link in the OP doesn't lead anywhere.
 
  • #4
PeroK said:
PS the link in the OP doesn't lead anywhere.
I do not know how to re-edt the summary.
 
  • #5
PeroK said:
Limit in what way? In SR the speed of a particle as measured in an IRF is limited by ##c##. Having an expanding physical object, if that is what you mean, doesn't change that.
I mean it purely mathematically.
 
  • #6
Ad VanderVen said:
I mean it purely mathematically.
I mean ##r(t) \, = \, b \, t## where ##t## represents time and ##0 \, < \, b##..
 
  • #7
Ad VanderVen said:
I mean ##r(t) \, = \, b \, t## where ##t## represents time and ##0 \, < \, b##..
And ##r## is the distance from the center of the sphere to a particle on the surface of the sphere (using an inertial frame in which the center of the sphere is at rest)?

Then ##\frac{dr}{dt}=b## is the speed of that particle using that frame. It will of course be less than ##c##.
 
  • #8
Ad VanderVen said:
I do not know how to re-edt the summary.
Report your post, include the correct link in your report, and one of us mentors can fix it for you.
 
  • #9
Ad VanderVen said:
I mean it purely mathematically.
There's no purely mathematical limit on the speed of a particle. But, if you apply the theory of SR, then there is a limit.
 
  • #10
Ad VanderVen said:
TL;DR Summary: Suppose we have an expanding sphere. That means that the surface ##4 \Pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b r##. Does this limit the speed at which a point can move on the surface?

Reference: https://www.physicsforums.com/forums/special-and-general-relativity.70/post-thread

Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?
So you are asking about the idea of an object that is confined to the expanding surface but which may be moving across that surface?

If the object is "coasting" across the surface, what happens to its speed as the surface expands? Does it retain its original tangential velocity? Or is its tangential velocity amplified by the expansion of the surface?

Neither physics nor mathematics can answer that question. Only clarification on the setup of the situation can answer it.
 

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