I was thinking about Newton's law. The case of changing mass is often ignored outside the textbook rocket problems. Are there and examples of the effect of an external force is to change the rest mass of an object while leaving velocity constant? I am familiar with something like in a particle accelerator in which particle are moving near the speed of light, but I do know that in relativistic mechanics, the measurement of "mass" is different from the rest mass. I'm specifically inquiring about phenomena in the classical regime, although I guest that classically, mass doesn't change.
In relativistic mechanics, "mass" is the same as "rest mass". The only example class I can see: If wind leads to erosion, a small fraction of the force is used to reduce the mass of the object in the wind.
What I meant was, in general, [itex]m = \gamma m_{0}[/itex], since [itex]m ≈ m_{0}[/itex] at non-relativistic speeds. Isn't wind erosion basically sand blasting though? Effectively breaking off pieces of rock (moving/accelerating them). Perhaps I'm thinking of it wrong. The more I think about this, the more I think it just really isn't possible because what I had in mind is some kind of field that would reduce the mass of a body placed in it. But where would the mass (elementary particles) go if it doesn't simply chip off? I guess it would be converted to energy or use some fancy quantum mechanical tunneling trick, but this would confound Newton. Maybe the problem comes from thinking of a mass as composed of many quanta as opposed to just a blob of stuff. Then it get's me imagining a bizzaro-world where the norm is for the mass to change and it's hard to think of a case where only velocity changes.
This "relativistic mass" is not used in physics any more. Right It is the same at rockets, you accelerate the exhaust away from the rocket.
Do you mean an external net force F on a body of total mass m wich centre of mass has velocity v? How could the velocity not vary, since F = ma (non relativistic regime)?
Velocity can remain constant since [itex]F = m \cdot \dot v + v \cdot \dot m[/itex] (even in non relativistic regime). It seems unusual but it corresponds to the original definition of force.
If [itex]v[/itex] doesn't vary, [itex]F = v \cdot \dot m[/itex] which means that the system's centre of mass varies and this is a different case from the one I asked, but I have understood better the OP' question now. If we are not necessarily talking of a linear trajectory but we can also consider an object spinning about a fixed axis, another example could do this: the object spins at constant angular speed while there is a constant non-zero axial torque on it, provided that the moment of inertia varies in the appropriate way.