What Happens to a Donut Spinning at Near-Light Speeds?

[Namloh2000]

donuts at the speed of light!

okay so as bodies approach the speed of light their mass gets bigger and bigger, approaching infinity - and their volume gets smaller and smaller, approaching nothing - a things length will get shorter and shorter as it approaches 186,000 miles per second - in the direction that the object is traveling.

OK - so let's say i had a donut that was spinning very fast, approaching the speed of light... what would happen knowing that things squish in the direction they are traveling as they approach the speed of light?

 

[Severian596]

They only squish relative to other reference frames. They do not squish as far as they are concerned. So...nothing?

 

[GRQC]

Originally posted by Namloh2000
okay so as bodies approach the speed of light their mass gets bigger and bigger, approaching infinity

This is not true. Their mass remains constant.

- and their volume gets smaller and smaller, approaching nothing - a things length will get shorter and shorter as it approaches 186,000 miles per second - in the direction that the object is traveling.

As it was pointed out, this is only an effect of reference frame dependence. In the donut's rest frame, it is a donut.

 

[Severian596]

Originally posted by GRQC This is not true. Their mass remains constant.

That's strange. So do you have a trick term or something up your sleeve that you're going to throw back at me when I say an object's mass DOES increase as its speed increases?

 

[GRQC]

Originally posted by Severian596
That's strange. So do you have a trick term or something up your sleeve that you're going to throw back at me when I say an object's mass DOES increase as its speed increases?

No, I'll just say that you're misinterpreting the equations. Mass is not a relativistic quantity. It is an invariant.

 

[Severian596]

Relativistic mass is not an invariant. Is relativistic mass only dialated from the perspective of other reference frames, too? I ask because I've seen floods of analogies for dilations of time and length, but not mass...

 

[DW]

Originally posted by Severian596
Relativistic mass is not an invariant. Is relativistic mass only dialated from the perspective of other reference frames, too? I ask because I've seen floods of analogies for dilations of time and length, but not mass...

"Relativistic mass" is not mass. It is a missnomer and has no place in modern relativity.

 

[Phobos]

Severian596 - Take a look through some of the older topics...there were several that presented the relativistic/invariant mass debate in depth.

 

[pmb_phy]

Originally posted by Namloh2000
okay so as bodies approach the speed of light their mass gets bigger and bigger, approaching infinity - and their volume gets smaller and smaller, approaching nothing - a things length will get shorter and shorter as it approaches 186,000 miles per second - in the direction that the object is traveling.

It's inertial mass (aka relativistic mass) increases with speed if that's what you mean. However it's proper mass is uneffected by speed.

OK - so let's say i had a donut that was spinning very fast, approaching the speed of light... what would happen knowing that things squish in the direction they are traveling as they approach the speed of light?

If the doughnut is rotating then this is a bit different than the situation you spoke of. The mass density of an object moving in a straight line increases as gamma². One factor of gamma is for the increase in mass and the second factor of gamma is for the increase in volume. But the situation you're referring to is different. E.g. suppose you restrain all particles of the doughnut to move at a fixed distance from the center of rotation. The volume of a doughnut will not change as measured in the inertial (non-rotating) frame. Otherwise the doughnut will expand due to centrifugal forces and at a certain point will fly apart especially at speeds approaching that of light.

But let's assume that all parts of the doughnut move in a circle at a distance which is independant of its angular velocity. Then the particle density does not increase and the volume remains fixed. The mass of the partices will still increase of course. The mass of the doughnut is the sum of the masses of all the particles so the mass of the doughnut increases as the doughnut's angular velocity increases. You can call this total mass the "rest mass" of the doughnut since the total momentum is zero.

I worked out a similar example using a rotating cylinder. See
http://www.geocities.com/physics_world/sr/rotating_cylinder.htm

Severian596 wrote

That's strange. So do you have a trick term or something up your sleeve that you're going to throw back at me when I say an object's mass DOES increase as its speed increases?

The only mass pertaining to a particle which does not increase with speed the particle's proper mass. The relativistic mass does increase with speed and this, of course, is the mass that Namloh2000 is referring to.

Phobos - This subject also came up recently regarding the mass of a rotating body.