# Does inertia increase with speed?

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?)

So inertia which is related to mass, increase with speed?

So, if I accelerate on a bus, my mass will increase and my inertia will increase for a while on the bus, until the bus stops?

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@nonagon How negligible is it? If it travels at 100km/h? – owlp May 15 '13 at 9:10
"The Inertia of Energy": mathpages.com/rr/s2-03/2-03.htm. The exact proportionality between the extra inertia and the extra energy of a moving particle naturally suggests that the energy itself has contributed the inertia, – Alfred Centauri May 15 '13 at 12:45
Please read en.wikipedia.org/wiki/… to the end of the section. – firtree May 15 '13 at 12:46

For both interpretations, the answer is 'yes' since force still acts in an opposite force on anything which has mass. As you accelerate, your velocity increases and therefore mass will increase. The increase in mass will bring about an opposite force. The greater the mass, the greater the inertia.

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It depends on how you define inertia. http://en.wikipedia.org/wiki/Inertia#Interpretations. The answer to your question is 'yes' if we interpret inertia as p=mv, and no if we interpret it as F=ma.

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If we interpret the inertia as $F=ma$, then 'yes' again: it increases with a factor of $\gamma$ in the transversal direction, and with a factor of $\gamma^3$ in the longitudinal direction. But if we interpret inertia as $F^\mu=ma^\mu$, then it does not change. – firtree May 15 '13 at 12:40
I'm confused, which is correct? I have read the Wikipedia, @Raindrop seem to be correct. I don't quite understand transversal direction, sorry. – owlp May 15 '13 at 13:44
The link for you again: en.wikipedia.org/wiki/… - and a good SR textbook is better that just Wikipedia, which is sometimes inconsistent. The "transversal" means "cross", and the "longitudinal" means "lengthwise", that is, the the cases when the direction of force is perpendicular or parallel to the direction of motion. – firtree May 15 '13 at 14:41
I didn't consider special relativity in my answer. – raindrop May 16 '13 at 5:47

I think It has more to do with acceleration than speed. What do you compare a constant speed to without knowing the inertial frame for the universe. For instance if the earth is traveling toward the constellation Leo at 390 km/s what would happen if you blasted off in a rocket in the opposite? After accelerating would you be moving 390 km/s or would you be sitting still compared to what you were doing?

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