What really is mass?

Greetings.  Today we'll be looking over a seemingly simple question but with many twists and turns: What really is mass? The concept of mass, (at least in my opinion) has never been clarified to the curious young physicists and it is important to delve into this significant property of an entity: mass.

Now the reason I wrote this article is due to the fact that I observed a lack in understanding of mass. In today's world, we consider learning as a play between complex statements; but that's exactly where this article shall excel: I shall not explain anything in complex terminologies, and shall enhance your foundations of Physics by looking at mass from a classical physics point of view.

So when I say that there is a lack of understanding in what is mass, this is what I mean:

Me: 'Hi Physics enthusiast. What is mass?'

Physics Enthusiast: 'Mass is the quantity of matter contained in a body'

Me: 'OK...And what is Matter?'

Physics Enthusiast: 'Matter is something that occupies space, has mass and can be typically perceived by our senses'

Really? Is that the definition? If we relate matter back to mass, we're essentially saying: 'Mass is the quantity of 'something that occupies space has mass and can be perceived by our senses'.' This is strange, it's like defining 'a' by telling it is equivalent to 'b' and defining 'b' by telling it's equivalent to 'a'.

So instead, join me on this endavour in finding the real definition of mass, a definition that works always(at least in the realm of classical physics) and a definition that is not vague defining itself back and forth.

So if we think of mass, we often relate it to weight and a reading we see on our weighing machine. And the weighing machine is as complicating to me as it is to you; on one hand it is called as the 'weighing machine' and on the other hand it presents the reading in Kilograms which is the SI unit for Mass and not Weight(which is a Force and thus its SI unit is Newtons) which is absurd, but that's the topic for another article. But yes, overall, we think of mass as a reading given by our Weighing Machine; but think...is that really what mass is?

We can also think of mass as the definition we see above but that is self-contradictory and inconsistent. Let's say we have an object, like water; the definition refers to that water's mass being the quantity of matter. Alright...and matter refers to something:

• That occupies space--OK, water occupies space

• Perceived by our senses--Yes, water can be perceived by our senses

• And has mass--That's what we're looking for! We're back at the start, so NO!

So this definition does not work as well as we might expect.

Instead, let's adopt a new definition. Mass is a measurement for the resistance to a force for a change in acceleration. Now don't run away, I'm going to simplify this whole thing for you. 

So if we have an object with mass m>0, then it means it should have some resistance to a force for a change in acceleration. Let's say the mass of this object is 1 kilogram and it is at rest and this object is a ball. For me to get this ball into motion, I need to apply little force and would also give up earlier to the force of friction. However, if I have say, a 30 Kilogram ball(that is destructive), I would need much more force to get it in motion, which means it has a higher resistance to force and would also move for longer before giving up to the force of friction. Thus, we can define mass as a quantitative measurement of the resistance the body by virtue has. This is the resistance to accelerate(or de-accelerate) due to a given force. That's a much more consistent definition of mass.

This is also consistent with Newton's 1st law of motion related to inertia. This property, what we just understood about the resistance to force is nothing other than intertia. So more the mass, more the inertia because mass is the quantitative measurement of inertia!

In fact, we can also perform mathematics in several cases for mass with Newton's famous equation:

F=ma.

We can use the above equation in representing our physics definition more mathematically so it's appealing and also to back up our claims. We rearrange the equation as:

m=F/a.

And what do we see by this? Well, we primarily see that the more the mass, the more the force required keeping the acceleration constant. Basically, it is backing up our argument about the fact that more the mass, more the force required since the resistance is greater. The same formula also tells us more the mass, lesser the acceleration from the same force and we see that if we rearrange the formula this way:

a=F/m.

Basically, more the mass, lesser the acceleration since the resistance to motion is increased. That's all logical...all that we did is represented all we were saying previously as words mathematically.