How to measure mass of a moving object in STR?

Question

I am a little confused about mass in STR.

In the rest frame of an object, you (A) can measure the mass using its operational definition i.e. from let's say a spring. Now for an observer (B) wrt. whom this mass moves at v. How can he measure its inertial and relativistic masses, like through which experiment? Also when he measures this would he find it as increased compared to A or same (ie whether it would be inertial or relativistic?)

EDIT:

A similar question is here already. There the answers focus on the definition of mass etc. What I have asked specifically is how to measure it? For instance, in the rest frame a mass can be measured by springs etc. An experiment or method that can measure it another frame. So basically I am seeing a body zooming past me, how do I measure its mass?

Then, when we measure this mass what will we get? (Previous answers I think say it will be an increased mass but don't give reason as to why then relativistic mass is getting abandoned) since if definitions were not made or the person measuring this mass didnt know the definition, for him this mass would be the actual mass and he will note it as a mass without knowing the difference between inertial and relativistic.

The previous question does pertain to the latter part of my question but I am looking for answers to the first and a little clarity on the follow up which is the second part of ny question

Answer 1

Relativistic mass and rest mass are both traditional concepts in physics, but the relativistic mass corresponds to the total energy.

The relativistic mass is the mass of the system as it would be measured on a scale, but in some cases this fact remains true only because the system on average must be at rest to be weighed (it must have zero net momentum, which is to say, the measurement is in its center of momentum frame).

For example, if an electron in a cyclotron is moving in circles with a relativistic velocity, the mass of the cyclotron+electron system is increased by the relativistic mass of the electron, not by the electron's rest mass. But the same is also true of any closed system, such as an electron-and-box, if the electron bounces at high speed inside the box. It is only the lack of total momentum in the system (the system momenta sum to zero) which allows the kinetic energy of the electron to be "weighed". If the electron is stopped and weighed, or the scale were somehow sent after it, it would not be moving with respect to the scale, and again the relativistic and rest masses would be the same for the single electron (and would be smaller).

In general, relativistic and rest masses are equal only in systems which have no net momentum and the system center of mass is at rest; otherwise they may be different.

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~Reference

• Mass in Special Relativity

Answer 2

It's quite simple to measure the relativistic mass of an object zooming past you: Grab a large greased board, and with that push the object.

To measure the transverse relativistic mass, you must all the time be pushing in the direction transverse to the motion of the object. (Note that in this process object gains no energy)

The longitudinal relativistic mass is larger than the transverse relativistic mass, and I have no idea how to measure it. Luckily the question was about relativistic mass, which term refers to the transverse relativistic mass.

pushing force = Instantaneous acceleration of object * rest mass of object * gamma