# What is the definition of inertial mass?

What is the definition of inertial mass? I can see two options, either it's the coefficient associated with the object being accelerated in Newton's 2nd Law, or it's the coefficient relating momentum to velocity. Or they are equivalent.

Well, if it is constant, then it's equivalent.

Inertial mass is the resistance that a body offers when a force tries to change its state of movement.

So it is the $m$ that appears here

$$p=m\dot{x}$$

and here

$$F=m\ddot{x}.$$

But if it's not constant you can see it as the magnitude that appears in

$$p=m\dot{x}$$

because in the force expression, there is a new term due to the mass variation. But the definition is the same.