# The speed at which a point can move on a surface?

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?

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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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.

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I do not know how to re-edt the summary.

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.

I mean it purely mathematically.
I mean ##r(t) \, = \, b \, t## where ##t## represents time and ##0 \, < \, b##..

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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##.

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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.

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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.

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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?