Are the inertia of two bodies of equal masses but different velocities same?

Question

if yes then why do inertia depends only on mass and not velocity like momentum

Answer 1

You are confusing two or three different concepts.

It *appears* that you have confused inertia *with* momentum - even though your question does indicate you know they are not the same. You might also be confusing it with Kinetic Energy.



But... Inertia is *not* mass (though it is a *property* of mass - and is so intrinsic to mass that they are *almost* synonymous), nor is it momentum (which, as you noted is dependent upon mass -&- velocity, nor is it Kinetic Energy ( dependent upon mass and velocity^2 )



Perhaps you are at an early stage of studying these concepts, so you are being confused from time to time. Remember - - some properties *are* ''interchangeable'' to some degree, even if *not* identical (Potential Energy & Kinetic Energy, for example...), others are very closely related, and in *some* cases might be considered identical - but in *others*, it is crucial to recognize the difference (such as *speed* and *velocity*) and others are very separate - but seem to be confused together over and over by beginning students (velocity and acceleration, for example)



And you are incorrect in your last statement. (well, at least in common Newtonian physics levels)

It takes exactly the same force (for the same length of time) to create exactly the same **amount of change** of state of motion with any two equal-mass bodies.

Feel free to do the maths. If you have problems, ask again - I'll give you a basic example to work through.

Answer 2

Inertia is a fundamental property of an object to other object in motion.



According to me, the answer to your question is 'YES'. Inertia depends on the mass of the object and not on its velocity. The magnitude of inertia is same for all velocities. Let us conclude with an example.

Imagine a boy of 40 kg weight is standing in a moving bus and a boy of the same weight is running here and there in the bus. And when the bus suddenly retards, both feel the same amount of inertia which is directly proportional to the retardation of the bus. Inertia depends on the speed of the bus and not on the speed of the boys.



Inertia depends only on mass and not on velocity like momentum because it is not a property of velocities of two different objects resting at a single object. Its magnitude is directly proportional to the velocity of the third object.

Answer 3

Inertia is the resistance of change in motion. It is, for all practical purposes, synonymous with mass.



More force is not required to change the state of motion of a body with higher velocity. It would take just as much force to increase the lower velocity body to the state of the higher velocity body as it would to decrease the higher velocity body to that of the lower.



And "inertial state of motion" is word salad.

.