# Momentum vs Inertia: Is Momentum a Measure of Resistance?

• Fez98
In summary, inertia and momentum are not the same thing. Inertia is the resistance of an object to change in its velocity and is proportional to mass. Momentum is the product of mass and velocity and is a measure of an object's amount of movement. It is not a measure of an object's inertia. Inertia is a conceptual quantity that is related to mass but is not exactly the same thing. It can be confusing and is often used as an alternative to the term mass in physics discussions. The concept of inertia was introduced by Johannes Kepler, but was later disproved by Copernicus and Newton, who showed that motion is the default state of all things and that external forces are needed to change this state.
Fez98
Hi. So I know that inertia (the resistance of an object to a change in its velocity) is reliant on mass. I also know that momentum is mass times velocity. So momentum is really inertia times velocity. My question is: if that's so, is momentum then not a measure of a moving object's inertia, its resistance to change in speed or direction? Please try to not get into really heavy answers, I haven't taken a single physics class, but this is a personal interest. Thank you :)

Fez98 said:
if that's so, is momentum then not a measure of a moving object's inertia, its resistance to change in speed or direction?

That's correct. Inertia and momentum are not the same thing.

Nick tringali
That's correct. Inertia and momentum are not the same thing.
Wait, so what IS momentum? If something has more momentum, it's common sense that it's harder to stop, or change direction. Like a truck going at 1 mph vs 120 mph

Momentum is amount of movement. Proportional to mass and proportional to speed.

Inertia is 'resistance' against acceleration. Proportional to mass only.

BvU said:
Momentum is amount of movement. Proportional to mass and proportional to speed.

Inertia is 'resistance' against acceleration. Proportional to mass only.
Yes, but something with a lot of momentum is hard to stop or change direction, right? So it seems that more momentum means its harder to change speed or direction

Fez, I don't think I can help you. You have an answer, but you don't seem to like it.

I agree. Are you familiar with Newton's laws ? ##\vec F = m\,\vec a\ \ ## can also be written as ##\vec F = {\displaystyle {d\vec p \over dt}}\ \ ## (in fact this is even a better form: it also holds true when ##m## is not a constant)

Fez, I don't think I can help you. You have an answer, but you don't seem to like it.

Fez, I don't think I can help you. You have an answer, but you don't seem to like it.
But then what causes my example to happen?

Fez98 said:
So it seems that more momentum means its harder to change speed or direction
No. Changing the speed of a mass of 1 kg with a speed of 1 m/s to a speed of 2 m/s is not 'harder' than changing the speed of a mass of 1 kg from 10 m/s to 11 m/s.

Fez98 said:
Yes, but something with a lot of momentum is hard to stop or change direction, right?
The same force will cause the same (rate of) change in momentum, regardless of speed. But for a faster object you need more change in momentum to bring it to a halt, or to change its direction by some degrees.

A.T. said:
The same force will cause the same (rate of) change in momentum, regardless of speed. But for a faster object you need more change in momentum to bring it to a halt, or to change its direction by some degrees.
Oh, OK, that makes sense, thank you

Fez98 said:
Oh, OK, that makes sense, thank you

In fact, momentum is not an absolute quantity of an object but depends on your reference frame. Imagine your truck going at 120mph and you put a wooden barrier in front of it. The barrier would be smashed. But, if you were in another vehicle going along beside the truck at 119 mph, and you put the same wooden barrier out, then the truck would only hit the barrier at 1mph and the barrier would just get a little bump as the truck overtook you.

This ties in with what you've learned that it is just as easy (or difficult!) to slow a truck from 120 mph to 119 mph as it is to slow it from 1mph to 0. And, in a fundamental way, these two scenarios are, in fact, identical. It's only the frame of reference that has changed.

Inertia is not really a concept that's needed when dealing with simple mechanics problems. Mass is a perfectly good quantity that describes 'how hard' it is to accelerate an objet (Newton's Second Law of motion)
The only time that I am aware of 'inertia' is when I really can't be bothered to get up off my backside and do those jobs that need doing around the house. In that context, 'mass' is not the right term to use.

Would that be a silverback-side ?

sophiecentaur
Inertia is a conceptual quantity that is rather unique in physics. It is *not* a physical quantity since it has no units. It's very much related to the physical quantity of mass but is not exactly ≡ same thing .

Inertia is a conceptual quantity that is rather unique in physics. It is *not* a physical quantity since it has no units. It's very much related to the physical quantity of mass but is not exactly ≡ same thing .
I think the term manages to confuse rather than to enlighten any argument. It's a sort of semi-official alternative to arm waving when it's introduced into Physics discussions. It allows one to step back from the implied rigour of using the word Mass and to let intuition to sneak in.

ulianjay
BvU said:
No. Changing the speed of a mass of 1 kg with a speed of 1 m/s to a speed of 2 m/s is not 'harder' than changing the speed of a mass of 1 kg from 10 m/s to 11 m/s.
It would require more energy though, would it not? force times distance.

sophiecentaur
Hi, i think the question is a very good one. My own findings from articles on the subject are, that originally Johannes Kepler introduced the concept of Inertia as "a property of an object to resist motion", this was at a time when it was thought that "rest" is the default state of things, and forces are needed to create motion. Later on, Copernicus and then Newton proved by the 1st Law that "motion" is the default state of all things in the universe, and in fact net external forces are needed to bring things to "a state of rest". With this , the 2nd Law said F = ma, => a = F/m where mass came to be referred to as "Inertial Mass". The mass became the fundamental property of matter . It defined the tendency of an object to get a "change in velocity per time" , when any Force acts on it. So, if mass is large, a = F/m should be a low acceleration.

The original question was :- is the Momentum a measure of an object's change in Inertia ?

Inertial Mass is not the same as Inertia. Mass is the correct term, and is the right straightforward measurable property. Of course, there are 2 kinds of definitions floating around- a) Gravitational Mass, and b) Inertial Mass. The latter, Inertial Mass, is considered the superior reference today, because it meausures "m" from " a= F/M" and not by using a weighing scale. Example, for a Space Station in orbit around the earth, due to weightlessness, there is no "g", and two different astronauts if put on a "weighing scale" will show the same reading , but we know this not correct. Hence, they use a special seat to apply some external Force and measure "a" , and from that, they measure the "m". This is Inertial Mass and not Gravitational Mass.

Coming to Momentum concept , I think that got really complicated by the Theory of Relativity. Copernicus in fact said that a ship that starts moving can continue moving around the Earth unless stopped by an external force. But later, in Einstein's two theories of relativity, the point was "provided we stand in a frame of reference such that the ship is seen to be moving" . What if our frame of reference is such that the ship appears stationary? Then Velocity will appear to be =0 , and the Momentum P = mv =0. Hence Momentum itself is not a good measure, rather Change in Momentum will be a good measure. That bring us back to acceleration , and Newton's 2nd law, a=F/m.

Actually, the ship could be moving with a Momentum from an Earth's frame of reference. To overcome this problem, it was agreed by scientists that " change in velocity per unit time " will be more reliable way to find Inertial Mass, as it will get detected by any frame of reference. That would work for normal objects which are not moving at speed of light etc etc .

Let me know if I am making sense.

Zachary Smith said:
It would require more energy though, would it not? force times distance.
Energy is frame dependent and that can involve some confusing scenarios.

But what do we mean by "harder" in this quote?:
BvU said:
Changing the speed of a mass of 1 kg with a speed of 1 m/s to a speed of 2 m/s is not 'harder' than changing the speed of a mass of 1 kg from 10 m/s to 11 m/s.
The momentum change would be the same but not the KE. The Impulse would be Force times time but the the Energy added would be Force times distance.

Zachary Smith said:
It would require more energy though, would it not? force times distance.

Good point!

It's worth having a think about this as it's trickier than you might imagine. For Earth-bound motion it's true that the faster you move, the more energy it takes to accelerate. And, the "harder" it is to accelerate. The key factor is the speed relative to the thing that you're using to propel yourself (e.g. friction on a road surface) and the effect of air and other resistance.

But, if you were in a vacuum and you propelled yourself by momentum exchange: throwing or firing things out the back of your spacecraft , then it would make no difference how fast you are traveling with respect to the Earth, say. (To keep it simple, let's consider non-relativistic velocities.)

If you look at post #8, it's interesting to consider what is the same in the two scenarios and what is different: you traveling at 119 mph and the truck at 120 mph; and you at rest and the truck traveling at 1mph. On the one hand, there is no such thing as absolute motion, on the other hand, they are clearly not the same.

Quite a little beside the present academic discussion:
How would Einstein calculate the rotational energy of a 6 kilometer long rigid bar with rest mass M rotating about its center with 15000 revolutions per second in gravity free space?

Jens said:
Quite a little beside the present academic discussion:
How would Einstein calculate the rotational energy of a 6 kilometer long rigid bar with rest mass M rotating about its center with 15000 revolutions per second?

I didn't see that one coming!

Jens said:
Quite a little beside the present academic discussion:
How would Einstein calculate the rotational energy of a 6 kilometer long rigid bar with rest mass M rotating about its center with 15000 revolutions per second in gravity free space?
So if you were spinning at the same rate along the same axis, you would say that the bar was not spinning, yet, your arms and legs will still fly off. Using that thought, could you then determine what would be stationary in space? On another thought, the term velocity seemed to be used very fast and loose. Velocity requires a speed and a direction as I remember from 1970's schooling.

Zachary Smith said:
So if you were spinning at the same rate along the same axis, you would say that the bar was not spinning, yet, your arms and legs will still fly off. Using that thought, could you then determine what would be stationary in space? On another thought, the term velocity seemed to be used very fast and loose. Velocity requires a speed and a direction as I remember from 1970's schooling.
I did not talk about velocity - only revs/sec.

Jens said:
I did not talk about velocity - only revs/sec.
Not you. Previous posters.

Fez98 said:
Wait, so what IS momentum? If something has more momentum, it's common sense that it's harder to stop, or change direction. Like a truck going at 1 mph vs 120 mph

Momentum is a conserved quantity, and it is a vector with a magnitude and a direction (in the same direction as the object's motion, i.e. as it's velocity, which is also a vector). In the realm of mechanics, changing an object's momentum requires the object's encounter with another object, with its own momentum, so that the sum of the TWO momenta remains constant. I believe that ONE definition of inertia is precisely this requirement for the input of 2 or more momenta to conserve overall momentum.

But what if the momentum of a particle is changed through it's interaction with an energy field? Within the domain of classical physics, no other object is required to accomplish this. Think of a moving electron changing direction in an electrostatic or a magnetic field. In this case, we may focus on the energy of the particle + field. Energy, unlike momentum, is a scalar quantity, depending on the particle's mass and speed (only the magnitude part of the velocity vector), and energy is also conserved. In this case, as long as it's trajectory is changing, the electron is under the influence of a force (another vector) which forces it to follow a curved direction. The force multiplied by the distance over which it acts is the work done on the electron, and that work equals the conserved energy of the system. My understanding is a bit fuzzy here, but I suppose the extra work/energy is extracted from electric field somehow. The QM explanation probably has to do with the interchange of photons between the electron's charge and the source of the electric field, but that's beyond the Phys 101 explanation I'm capable of giving. If you had to calculate the electron's trajectory, you could begin by solving Newton's inertia equation for the acceleration: a = F/ m. The inertia, given by the acceleration, is thus proportional to the force required to generate the acceleration. The incremental work done on the electron is the product of the magnitude of the force on the electron and the incremental distance: dW = F ⋅ da. Adding up all these dW s (or using calculus to integrate them) gives you the total work and thus the total change in the energy.

Momentum is the name of a quantity and appears in many equations. Inertia is the name of a concept and not concrete thing. It basically means the conservation of momentum. So you don't see "inertia" as a variable in any equation, but you might hear an explanation of something as due to inertia.

sophiecentaur
It's quite interesting, your question. Not looking at things too technically, I think you're right. You can think of momentum as the inertia of a moving body ( or the other way round also).

## 1. What is momentum and inertia?

Momentum and inertia are both physical concepts that describe the motion of an object. Momentum refers to the quantity of motion an object has, while inertia refers to an object's tendency to resist changes in its motion.

## 2. Is momentum a measure of resistance?

Yes, momentum can be considered a measure of resistance because it describes an object's tendency to continue moving in the same direction and at the same speed.

## 3. How are momentum and inertia related?

Momentum and inertia are closely related because inertia is a property that affects an object's momentum. The more inertia an object has, the harder it is to change its momentum.

## 4. Can an object have momentum without inertia?

No, an object cannot have momentum without inertia. Inertia is a necessary component of momentum and is a result of an object's mass and velocity.

## 5. Which is more important in determining the motion of an object: momentum or inertia?

Both momentum and inertia are important in determining the motion of an object. Momentum determines an object's speed and direction, while inertia affects how easily the object's momentum can be changed.

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