# Donuts at the speed of light

1. Mar 17, 2004

### 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 lets 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 travelling as they approach the speed of light?

2. Mar 17, 2004

### Severian596

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

3. Mar 17, 2004

### GRQC

Re: donuts at the speed of light!!

This is not true. Their mass remains constant.

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

4. Mar 17, 2004

### Severian596

Re: Re: donuts at the speed of light!!

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?

5. Mar 17, 2004

### GRQC

Re: Re: Re: donuts at the speed of light!!

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

Last edited: Mar 17, 2004
6. Mar 17, 2004

### 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...

7. Mar 23, 2004

### DW

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

8. Mar 23, 2004

### Phobos

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

9. Mar 23, 2004

### pmb_phy

Re: donuts at the speed of light!!

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.

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 refering 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

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 refering to.

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