What are the "masses"?

I know there are three "masses".

"inertial mass", based on Newtonian Mechanics

"rest mass" and "relativistic mass", based on relativity

Anyone can explain three of these in a relatively easy way? I'm confused

Newtonian inertial mass is based Newtonian mechanics, which is invalid, to an extent, as per Einstein's relativity. It is still valid for most application in common everyday scenarios. It is defined as the mass that gives resistance to acceleration. It is the mass that will come in $$F = ma$$.

Rest mass is the mass that an object has at rest. It does not include the mass(/energy) that it gains due to velocity. This mass does not change irrespective of the environment, the velocity, etc.

Relativistic mass is the mass that the object has in total, which includes the rest mass, and in addition the mass it has in virtue of energy, including kinetic energy. The total mass is given by

$$m_{rel} = \frac{m_r}{\sqrt{1-\frac{v^2}{c^2}}}$$

where $$m_r$$ is the rest mass and v is the speed with which it is moving. Derivation to this formula uses more of relativity.

However, it is this mass (relativistic mass) that is to be used in all formulae, when the velocities are large. At small velocities, the denominator is approximately 1, and hence the relativistic mass and rest mass are nearly the same. When the velocities are almost that of the speed of light, the denominator is nearly 0, and hence the relativistic mass approaches infinity. Henci it becomes increasingly hard to accelerate past that.

Hope this helps.

• Actually the 'relativistic mass' is not a good concept in my opinion. It depends on the observer, and it is not equivalent with the rest mass. (As pointed out in some of the answres here.) (The relativistic mass is actually the total (kinematic and rest) energy of the particle.) Commented Aug 30, 2020 at 15:21
• It is still essential in explaining certain phenomenon like c being the absolute speed limit, etc. and is hence essential. Commented Aug 30, 2020 at 15:26
• @ManishS Is the "rest mass" something like "absolute mass"? Since it can't be affected by anything Commented Aug 31, 2020 at 6:19
• In that sense, yes. Commented Aug 31, 2020 at 10:08

The mass that most theoretical physicists used is 'invariant mass', defined by $$m^2=E^2-{\bf p}^2$$ in natural units with c=1. This avoids confusion arising from 'relativistic mass' which is different in different directions and different Lorentz systems.