Can someone clarify if the mass of an accelerated particle increases, and if so, is this just a mathematical increase or is it a measurable increase? If it’s measurable, how is it measured?
Thanks for any help with this!
Relativity tells us that the mass of a body approaches infinity as the body accelerates towards the speed of light. This is measured by the amount of force needed to increase it’s velocity above its present value.
mr = m/sqrt(1 - (v/c)^2)
where m= the mass measured in the same inertial reference frame as the observer (ie, when neither is moving relative to the other).
So, the mass of a body, as measured by an observer, is related to how fast that body is moving (speed, not acceleration) relative to the observer. Different observers, however, will measure different values if they are moving at different velocities.
IOW, it’s all relative. 
If it was acceleration that affected the mass, anything going in circles would constantly be changing its mass, since it’s always accelerating.