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There are several kind of forces in the world.
Is there only one kind of mass of an object in this world?

If so, why?

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Indeed, there are two notions of mass: the inertial and the gravitational mass.

The inertial mass $m_i$ is the mass which tells us which force $F$ is necessary to achieve a certain acceleration $a$: $F=m_i a$

The gravitational mass $m_g$ is the mass which tells us how strong the gravitational interaction to other masses is: $F=G\frac{m_g M_g}{r^2}$

According to the equivalence principle the masses are, however, equal: $m_i=m_g$. This is confirmed experimentally with very high precision.

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  • $\begingroup$ Is there only one kind of inertial mass of an object in this world? Can I call the gravitational mass the gravitational charge? Thank you for your answer. $\endgroup$ – tchappy ha Jan 23 at 10:34
  • $\begingroup$ If I call the gravitational mass the gravitational charge, then there are several charges in this world. Electric charge, gravitational charge, magnetic charge. But Is there only one kind of inertial mass in this world? $\endgroup$ – tchappy ha Jan 23 at 10:38
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    $\begingroup$ Yes, there is only one kind of inertial mass. Charges quantify the strength of the different interactions. Since there are four known interactions, there are also four types of charges (including gravitational mass). However, Newton's laws of mechanics are universal and unique, so there is only one way to connect force and acceleration, not several. $\endgroup$ – Photon Jan 23 at 12:03
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    $\begingroup$ @tchappyha Sure, you could rename the terms if you wish and call them gravitational charge and electrical charge instead of gravitational mass and electrical charge. That is just about naming convention, and if you can convince the rest of the World to change the name, then go for it. But no matter if you call it gravitational mass or gravitational charge, it doesn't change the fact that it is an entirely different concept from inertial mass. There is only one type of inertia that we know of. $\endgroup$ – Steeven Jan 23 at 12:08
  • $\begingroup$ However you won't have gravitating bodies with opposite charge so why rename it? $\endgroup$ – Alchimista Jan 24 at 10:07

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