Momentum vs inertia

[Galaxion]

TL;DR

Momentum physical meaning

Can momentum considered as the resistance of a force? Why?I noticed that the physical meaning of momentum and inertia are similar

 

[russ_watters]

No, I don't think so. Inertia (mass) could be considered resistance to acceleration due to applied force via a=f/m. I'm not even sure what "resistance of a force" would mean physically/mathematically.

 

[Ibix]

Inertia is how hard it is to make something change its state of motion, which is essentially mass.

 

[Matterwave]

A body at rest still has inertia even though it has no momentum.

 

[sophiecentaur]

A body at rest still has inertia even though it has no momentum.

Momentum is frame dependent; the velocity is relative to a reference velocity. Your "rest" is not a particularly special situation (to a Physicist).

Mass is not frame dependent. Mass and Inertia are pretty much in the same neck of the woods and the use of the words depends on the context and the audience when 'explaining' the same phenomenon.

 

[wrobel]

TL;DR: Momentum physical meaning

Can momentum considered as the resistance of a force? Why?I

I doubt that the answer to your question, whatever it may be, will help you in any way when setting up the system's equations of motion.

 

[Herman Trivilino]

the resistance of a force?

There's no such thing as resistance of a force.

 

[Dale]

TL;DR: Momentum physical meaning

Can momentum considered as the resistance of a force?

I think that would be mass. Resistance comes from Ohm’s law: $V=RI$. If you analogize a force in Ohms law you would probably say a force is analogous to the voltage.

In Newton’s 2nd law you can write it in terms of momentum $F=dp/dt$, but that doesn’t clearly map to Ohm’s law. But if you write it in terms of mass then $F=ma$. This more clearly maps to Ohm’s law with force mapping to voltage, acceleration mapping to current, and mass mapping to resistance.

 

[Paul Colby]

Also, for Ohms law, current flowing through a resistor dissipates energy in the form of heat. For Newton, force goes into kinetic energy. This process is reversible. A closer mechanical analogy would be a loss term $F=-\alpha \frac{dx}{dt}$.

 

[Herman Trivilino]

I noticed that the physical meaning of momentum and inertia are similar

Can you expand on this a bit? In what way are they similar?

To most people inertia is synonymous with mass $m$.

Momentum is $m \vec{v}$, where $\vec{v}$ is the velocity.

Note that mass is a scalar quantity whereas momentum is a vector quantity.

 

[sophiecentaur]

Resistance comes from Ohm’s law: V=RI.

When trying to use an analogy to explain something then it is important that the analogy is valid. Ohm's Law states that the ratio of V/I is constant for a metal at constant temperature. That ratio is referred to as the Resistance. Merely quoting the ratio of volts to current in any old conductor is not "Ohm's Law" because V is not always proportional to I. I have come to terms with this sloppiness being common on PF but, in this context you really have to question the validity of quoting Ohm's law. It's rather the reverse actually: Newton's second law is a law because mass doesn't change but an invariant Resistance is a very rare occurrence.

This is really not just being picky.

 

[Yug Ahuja]

TL;DR: Momentum physical meaning

Can momentum considered as the resistance of a force? Why?I noticed that the physical meaning of momentum and inertia are similar

momentum and inertia aren't the same quantity!

lets talk about momentum first
The best definition of it as i know is 'the amount of motion'. This quantity remains conserved in an isolated system. it changes when an external force acts on the system
And the beauty of this definition is that it directly relates to the formula,
what should be the amount of motion proportional to?

distance? but in one system particles may have travelled more distance but might be in rest now and in the other system particles might have travelled less but maybe they are travelling at greater speed now
so it might be wiser to use speed as the quantity instead of distance

a system with more mass will have more quantity of particles executing the same motion so amount of motion must also be proportional to mass


call this thing p, now $p \propto mv => p = mv$ ( i cant think about any third thing it will be proportional to, if u think about one, let me know)

now just think about what a force do, it add or subtracts to the amount of motion of a system. force is the time rate of change of amount of motion of a system so u get newton's second law

now about inertia
inertia is more of an abstract term, basically the resistance to motion or a better way to describe it as a reducing factor for motion

in linear kinematics, all particles have same acceleration as COM, so it implies every dm element of particles resisted equally to force and got equal acceleration
here, if u call inertia I, then I = M, M is the mass of body
and as u can see $a = F/M = F/I$ , inertia acted as a reducing factor or resistance

in rotational kinematics, if u think, the particles further from axis, resists more to rotation, they therefore have more inertia even when they have the same mass
so inertia is weighted by distance. $I ≠ M. I = MR^2$ ( I am not going for derivation here)
and thus $\tau= Mr^2 \alpha$ , as u can see rotational force required scales by $r^2$ factor

 

[sophiecentaur]

inertia is more of an abstract term, basically the resistance to motion

The word 'resistance' has an implication of energy loss - as in electrical and frictional resistance. If you really want to use a form of words then why not 'reaction' (like Sir Isaac).

But, seriously, this is really not a physics thread. It's semantics. Physics and Engineering get along fine without using the term Inertia so why spend too much time discussing it in terms of those fields. Obviously the word Inertia has a wealth of meaning in the context of human behaviour (laziness and established belief and ideas etc.) so it's probably best to stick with its very valid use in that context?

 

[Yug Ahuja]

Thanks for the feedback, sophiecentaur.
You're absolutely right that in mathematical physics and engineering, we dump the word "inertia" and just stick to $(m)$ and $(I)$ to avoid ambiguity. My goal was to look at it from a pedagogical standpoint. Textbooks frequently introduce Newton’s First Law as the "Law of Inertia," which is why learners naturally try to map a physical intuition to it before jumping straight into the math. Many books also categorize Inertia into inertia of rest, motion or rotation. I, myself, was confused first between 'inertia of motion' and 'momentum'. They seemed the same thing.
Good point on the word "resistance" implying energy dissipation. A better phrasing on my part would have been "inertia represents a system's quantifiable opposition to acceleration," rather than a dissipative resistance.

 

[sophiecentaur]

I, myself, was confused first between 'inertia of motion' and 'momentum'.

Well - there you go. A very good reason not to include inertia in Physics teaching. Otoh, if a student brings up the word there it can be dealt with appropriately, stressing that it's not a term that's used today, for good reasons.

There's a very suitable analogy with the reaction of an electrical inductor but that's some way down the road from Newton and mechanics.