ccb056 wrote:Would the mass become infinite if the linear velocity is less than the speed of light, no.
isn't the whole point that some of the paddle will have a linear velocity faster than the speed of light? - those sections will have infinite mass (and the sections nearby will be getting pretty close to infinite mass too). you can't be moving just parts of the paddle at once (the parts going less than C), you have to move the whole thing and if only some of the paddle has infinite mass then as far as inertia is concerned the WHOLE THING has infinite total mass.
you can't just move part of it (the part going less than C), the whole thing has to be moved.
sure, you have a car going less than the speed of light - but it's dragging an infinite weight trailer. it's going nowhere.
DCrazy, if you have a roatting paddle, the closer you get to the center, the closer the angular velocity gets towards infinity, it has to past the speed of light somewhere
With any rotating body, as you get closer to the pivot, the angular velocity increases, in fact, it increases to infinity. At the pivot point, the angular velocity is infinite, this is true for all rotating bodies.
The angular velocity for any point is between infinity and the linear velocity of an outer point. So, somewhere in between is an angular velocity that is greater than c.
That is why E=MC^2 doesnt apply to angular velocities, if it did, it would be impossible to rotate a wheel.
E=mc^2 applies too all matter. the formula is simplified way of saying that matter and energy are the same thing.
Remember, c in that equation is a universal constant; not a varible for an unknown velocity.
That being said... angular velocity(and thus angular acceleration) remains constant thru all points of the radius of a circle - its mesured in radians per unit(hence, the angular) time, not distance per unit time.
An object rotatining around point P is rotating at a rate of 15 degress per second will have its speed reduced as it approaches the centre of the circle because the distance covered is reduced accordingly.
"The mass of the different pieces will increase as they move towards the speed of light." Dcrazy
So you are saying what? The size of the object swells up as it approachs c?. If so does velocity then affect the spacing between atomic particle that comprise the object? Or are we talking about something akin to the tranmutation of lead into gold?
I said mass, woodchip, not volume. It's a corrollary of mass-energy theorem. By virtue of Einstein's equation E=mc^2, the total energy of an object is directly proportional to its mass. If you accelerate an object to a velcoity very close to c, mass-energy dictates that its mass increases without bounds (i.e. towards infinity).
ccb056, you are completely neglecting the fact as the speed of a piece of mass approaches c the mass of the object approaches infinity. Therefore to accelerate past c two impossible things have to happen:
1. The object's mass must be greater than infinity.
2. The energy supplied to the object must be infinite because the object's rotational inertia increases without bound.
