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Physicsguru
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Suppose that nothing in the universe existed, except for one solitary billiard ball. For the sake of definiteness, let it be an eight ball.
So the center of mass of the universe is the center of mass of the eightball. Now, the eight ball has an inerital mass m, which is either a function of its speed v in a frame or not. Suppose that m(v), therefore m=m(x,y,z,t) in general. OK so now here is my question. Suppose that in a frame of reference where the center of mass is at rest, and the location of the number 8 on the surface of the solid spherical billiard ball is at rest, the rest mass is exactly m0. What would be the total inertial mass of the billiard ball in a reference frame in which the center of mass was at rest, but the number 8 was orbiting the center of mass with tangential speed v?
For clarity, let the radius of the billiard ball be R. You can presume that R(t) or not, that's your choice depending on how you want to handle temperature, and radiation, etc.
Regards,
Guru
PS: This is supposed to be an ordinary 8 ball. You can presume that the density is constant if you want. You can presume the net electric charge is zero if you want or not. And you can start off by assuming the formula for relativistic mass is correct.
If you want a model for the interior structure of the eightball, pretend that its basically a lattice structure, and that the total number of molecules is N.
[tex] m = \frac{m_0}{\sqrt{1-v^2/c^2}} [/tex]
So the center of mass of the universe is the center of mass of the eightball. Now, the eight ball has an inerital mass m, which is either a function of its speed v in a frame or not. Suppose that m(v), therefore m=m(x,y,z,t) in general. OK so now here is my question. Suppose that in a frame of reference where the center of mass is at rest, and the location of the number 8 on the surface of the solid spherical billiard ball is at rest, the rest mass is exactly m0. What would be the total inertial mass of the billiard ball in a reference frame in which the center of mass was at rest, but the number 8 was orbiting the center of mass with tangential speed v?
For clarity, let the radius of the billiard ball be R. You can presume that R(t) or not, that's your choice depending on how you want to handle temperature, and radiation, etc.
Regards,
Guru
PS: This is supposed to be an ordinary 8 ball. You can presume that the density is constant if you want. You can presume the net electric charge is zero if you want or not. And you can start off by assuming the formula for relativistic mass is correct.
If you want a model for the interior structure of the eightball, pretend that its basically a lattice structure, and that the total number of molecules is N.
[tex] m = \frac{m_0}{\sqrt{1-v^2/c^2}} [/tex]
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