# What is the different between momentum and inertia?

## Recommended Posts

I have a basic question. My science teacher is talking about momentum and inertia because we are going over the laws of motion, and he gives us the formula for inertia for the first law, which is I=mv, and then he gives the equation for momentum, which is p=mv. Why are the equations the same for momentum and inertia? My science teacher just said that inertia is a property of a unmoving object, and momentum is a property of a moving object. I get that, what I don't get is why, quote "Inertia stays in an object even when it is moving, but momentum goes away when an object is not moving." So to clarify, what he said is Inertia will be in an object no matter what, moving or not, and momentum is only in an object that is moving, and it isn't there when it isn't moving. So why do scientists need to have two words? Or is my science teacher wrong and just wasn't in the mood to tell me something.

Oh, and another quick question. How can something not have any mass? I know that a photon, the particle that carries light, or creates it, has no mass, so according to the second law of motion, it cannot acceleration, therefor it travels at a constant speed no matter what. But why does it not have any mass? How is that possible? Or does it have no mass because it's mass is to small we can't detect it.

And my last question of the night, I know that light travels at about 300 million m / s. What decided that it travels at that speed?

##### Share on other sites

Inertia is a bit of a nebulous concept/property. The meaning depends on the context of how it's used. The principle of inertia is that objects don't change their motion, which includes being at rest, unless acted upon by an outside force. In that way, it's like mass, which quantifies how much the change in motion (acceleration) is resisted by a given force. But of you look at it as the resistance to a force, i.e. what changes when a force is exerted, then it's like momentum. Again, the context matters.

Newton's laws of motion are classical, but one also needs to know that the second law is F = dp/dt (you can derive F=ma from this under the assumption that mass doesn't change and is nonzero). To see more detail of nonzero mass you have to look at relativity.

##### Share on other sites

I=mv, and then he gives the equation for momentum, which is p=mv. Why are the equations the same for momentum and inertia? My science teacher just said that inertia is a property of a unmoving object, and momentum is a property of a moving object.

Surely anyone who says I=mv then says the object is 'unmoving' (v=0?) should offer a better explanation, since by this definition I=0 for all objects at all times.

I must respectfully disagree with swansont. It is mass not inertia that is the more nebulous. Inertia is a very precisely defined quantity but rather complicated; mass is more difficult to pin down.

I don't know whether you have yet covered vectors and scalars in your course, but mass is a scalar.

Velocity is a vector and we can multiply any vector by a constant or scalar (which is just a constant number) to get a new vector.

So your statement p=mv is a vector equation.

If we multiply the vector velocity by the mass we get another vector we call the momentum.

The momentum vector has the same direction as the velcoity and a magnitude equal to the product of the mass and the magnitude of the velofity vector.

The complication arises because there are two 'sources' of mass in the universe.

Gravitational mass, which is due to the attractive force object exert on each other.

Inertial mass which is the resistance of an object to an applied force.

It was a very important milestone in physics to show that these two masses are numerically equal.

That is to say that any force, gravity or otherwise, will have the same disturbing effect on an given object.

Now the momentum equation considers the object as a 'point mass'. That is it considers the object to act as if all the mass were concentrated at a single point.

Of course in real objects the mass is distributed thought the volume taken up by the object.

And a disturbing force can be applied in many ways. Slowly, rapidly, distributed across the object, at one corner and so on.

The full definition of Inertia allows us to account for all this to calculate what happens when a force is applied. That is does it spin, twist, move off line, or what?

The maths of this is quite complicated and not normally covered in basic courses.

Inertia is not a vector and not a scalar.

##### Share on other sites

Now the momentum equation considers the object as a 'point mass'. That is it considers the object to act as if all the mass were concentrated at a single point.

I am a bit puzzled by this. If a body of finite size and of mass m is moving with a velocity v, I would expect its momentum to be mv. I can't see why it is necessary to regard the body as a point.

If a non-uniform field of force is acting on the body, the effect of the force might vary from one point within the body to another. But I don't see what this has to do with the definition of momentum.

Personally, I have always considered "inertia" to be a vague term referring to a resistance to a change in velocity.

Edited by JonG
##### Share on other sites

I am a bit puzzled by this. If a body of finite size and of mass m is moving with a velocity v, I would expect its momentum to be mv. I can't see why it is necessary to regard the body as a point.

Let us say you have a train comprising a locomotive of mass ml pulling a carraige of mass mc at velocity, v via a long chain.

What is the momentum of the train?

The locomotive runs into the buffers. What is the momentum of impact?

##### Share on other sites

Let us say you have a train comprising a locomotive of mass ml pulling a carraige of mass mc at velocity, v via a long chain.

What is the momentum of the train?

The momentum of the train would be (mI + mc).v

The locomotive runs into the buffers. What is the momentum of impact?

I'm not sure what "momentum of impact" means. The force exerted on the buffers arising from the change in momentum of the locomotive during the short period of time encompassing the collision could be found from the change in momentum of the locomotive. The change in momentum of the locomotive would be mI.v, if the locomotive were brought to rest.

But what has this got to do with defining momentum in terms of point-like particles?

## Create an account

Register a new account