Cylinder on frictionless surface

If there is no friction, then how does it roll?

So if there is no friction, how long will the cylinder slide? ... since there is no force impeding it, then it will continue with the same velocity forever: Newton's First Law of Motion.

If there is some force opposing it - well if you know all of the numbers, then you can calculate when it will stop.

 

If you leave a cylinder in vaccum with only traslational velocity , it would continue moving without stopping for infinite period of time( remember, there is no force to slow the motion of the cylinder as you have assumed that there is no air drag/friction), moreover it won't develop any rotational velocity in due course of motion.
If you leave it with a non zero rotational velocity and and translational velocity , it will continue to remain in this state.
Now if you applied a force , then it will de-accelerate the cylinder, with a=F/m.
Secondly the applied force will provide a torque about the centre of mass of the cylinder. Torque=F*(r-R)/(M*(r^2)/2). Where R is the radius of cylinder , and r is the perpendicular distance of the point of application of force with ground. This may increase or decrease 'alpha' depending on the value of r. Take a note-'Changing v will not change 'omega' is this case or vice-versa '

 

first of all lets say a ball rather than a cylinder as with a cylinder we usually think something different but that doesn't matter that much as the physics stays the same no matter what the object.

In order for something to be " frictionless" it has to be in vacuum and it cannot touch anything else , pretty much like planets orbiting in our solar system , held up by gravity so they don't have to be held up by some physical object like our human devices have to.
gravity is not the only force that can hold something up with " no strings " attached. magnetic and electric fields can do that too , magnetic being the best example.maglev train etc , but that requires some energy input.
But remember physical friction between two bodies or the friction between a moving body and air or any other gas is not the only thing that can de-accelerate or accelerate an object , fundamental fields tend to do just that too , like gravity , electric or magnetic field. For example you can accelerate a metal ball with the help of a magnetic field where the force of acceleration would be the greatest the closer it gets to the source of the field.
Gravity too tends to change the speed of things , like it slows down light which is called redshift.

as for the speed of light no friction , infinity thing it goes like this , in order for something to have certain speed aka to move at all it had to get that momentum at the beginning from some force etc.Once it got that if there is or was or will be nothing in the way to stop or slow it down it will continue to fly or roll or do whatever it does forever and ever. If you want that something to go faster now to go forever with the speed which would be close to the speed if light you have to accelerate it , push it in other words give it some extra energy so that it would move faster.A car doesn't speed up on itself it requires engine torque and gasoline aka fuel to do that so energy must be supplied.Once it' s done and f there is nothing to slow it down it will continue to move forever at this now greater speed the object gained while you were " pushing" it.Got that?

By the way physical objects which have mass can' t get to the speed of light they can get close but not at the speed of light.
Light itself being electromagnetic radiation is kinda weird it has energy (sometimes alot of it) but it itself has no mass or what science calls restmass , with that one means that light doesn't weigh anything , you can bombard a metal plate with photons , in other words keep it in sunshine for a while and it will not get heavier just hotter which is a example of light having energy which it imparted in that plate when it hit it.

 

If a positive force is applied - perhaps light pressure, or solar wind - then the object will speed up. If it is unopposed it will gain speed. Under these circumstances it will approach tthe speed of light ... but it will never get there.

But .9c or .999c is possible - like cosmic ray particles.

 

i feel your second point is not a matter to think about as it's practically impossible,
though i've not learnt quantum one cannot judge with most accuracy and no experimental proof
'c' is something like ∞ i.e. it cannot be reached
mind me saying it may be wrong

 

Mind you, it takes longer and longer to gain speed with a constant force.

For example, 20,000 volts will move an electron from standing to .25 c over a short distance. But 30,000 volts only gets the electron to .33 c.

The calculations are easy ... any boook on relativity will show how. I suggest Taylor and Wheeler... Spacetime Physics. It only requires algebra, patience, and some effort.

 

Crazy, I believe this is incorrect. If it is hotter it has more energy, and it is therefore heavier.

 

Correct ... as you add internal energy to an object it gains mass.
As it cools it will radiate away the extra energy, and lose the mass.

These amounts are quite small.