# The Concept of Mass

1. Aug 28, 2011

### IWantToLearn

Hi all

I am wondering about the concept of Mass in physics. What does it mean? , why we have different concepts of mass? , Why scientists anciently proposed two concepts of mass, inertial mass and gravitational mass? , Why they wondered if they are equivalent, while if i was a one of their contemporaries I will accept the idea that they are the same thing as intuitive thing and I will never ask if they are equivalent?

Thank you for helping

2. Aug 28, 2011

### I like Serena

Welcome to PF, IWantToLearn!

Mass is a measure of inertia.
This is demonstrated in Newton's law F = m a, where the mass is the constant that relates force to acceleration.

This is different from gravitational mass, since that is the constant that relates how strongly 2 masses attract each other.

So on the one hand we observed that it takes more force to accelerate a greater mass, while on the other hand we saw that a greater mass attracts another mass more strongly.

By choosing the gravitational constant G appropriately, these two mass concepts turned out to be the same.

3. Aug 28, 2011

### Jodo Kast

I've always been under the assumption that mass is what objects have irrespective of gravity. And weight is what objects have when subjected to gravity.

I don't recall having heard that mass is a measure of inertia. It's pretty obvious (now), yet more difficult for me to visualize than thinking solely in terms of gravity. I guess it's because the word "gravity" is used in everyday speech (by non-scientists) far more often than "inertia". People can easily talk about gravity even if they don't understand it, but "inertia" is a scary technical word that carries with it a pinch of erudition.

4. Aug 28, 2011

### IWantToLearn

i understand that mass is a number that represent the amount of matter, now i can see that you are talking about mass from the perspective of dynamics and gravity, some other perspectives like quantum mechanics, relativity have different concepts for mass
Now why we try to define mass using these perspectives instead of sticking to the most intuitive definition " amount of matter"

5. Aug 28, 2011

### I like Serena

Matter "resists" getting to move, and it also "resists" getting to stop.
This is what is "inertia" means.

If you want a certain amount of matter to "get moving", it should be intuitively clear that it takes twice as much effort (force) to get a double amount of matter moving.
So given a certain acceleration, force and "amount of matter" are linearly correlated.

Similary a double amount of matter generates an attractive force that is twice as big.

However, an "amount of matter" is not clearly defined yet.
Typically this would be the number of molecules, but different molecules have different inertia (that is different mass).
So we need to multiply the number of molecules by the material-specific molecule-mass to find the "constant" between force and acceleration.

6. Aug 28, 2011

### jishitha

Hi everybody, what is the concept of moment of mass? And what is the relation with centre of mass...?

7. Aug 28, 2011

### I like Serena

Let's start with center of mass, and see if I can get the concept across in a manner that satisfies you.

When you push against an object, the object will tend to move as well as turn.
If you push in the direction of its center of mass, it won't turn, but only move (translate).

If you hold an object on one of its edges and let gravity do its work, the object will start turning until its center of mass is immediately below the point where you're holding it.
By repeating this with different points, the center of mass can be pinpointed.

8. Aug 28, 2011

### I like Serena

As for moment of inertia, this works as follows.

Let's say we fix the object with an axis, so it can only turn and not move.
When a force is exerted to that object, which is not in the direction of its axis, it will start turning, and it will accelerate doing so.

The angular acceleration depends on two things: the force, and the distance of that force to the axis.
We call the product of the two the "torque" (or the "moment").

The ratio between the torque and the angular acceleration, is the moment of inertia of that object.

9. Aug 28, 2011

### IWantToLearn

I think that i got it, although that mass is something that we can percept and feel, even measure, and it looks like a very intuitive thing, it is very hard to define, because defining it in terms of matter, make the problem of definition even harder and more mysterious, because matter itself is not clearly defined, one thing to add is that not only matter exhibits mass property, also energy exhibits mass properties
i got this from the wiki

"Mass must be distinguished from matter in physics, because matter is a poorly-defined concept, and although all types of agreed-upon matter exhibit mass, it is also the case that many types of energy which are not matter—such as potential energy, kinetic energy, and trapped electromagnetic radiation (photons)—also exhibit mass. Thus, all matter has the property of mass, but not all mass is associated with identifiable matter."

http://en.wikipedia.org/wiki/Mass

now i can understand why scientists anciently differentiate between two types of masses, inertial mass and gravitational mass, and that is why they were wondering if they are equivalent.