Mass and Inertia

in your study of physics you will often encounter the idea of mass and you will also might encounter the idea of inertia and what I want to do in this video is think about what is the similarity or the difference between these two concepts or these two ideas and physics and I'm going to give you a little bit of time to do it I encourage you to ask people and search the web and look at textbooks whatever you can do to figure out the similarities and differences between mass and inertia so from a historic perspective if you've asked for someone what is mass mean or what does it represent they'll say it means what it represents how much stuff an object is made up of or how much matter how much matter actually constitutes an object and if you were to ask them well what is inertia then they'll say well inertia describes an inertia is a property of an object that's really how hard is it to accelerate that object how hard is it to change that object's velocity so we could call this maybe a resistance resistance to acceleration so on this first this first glance right over here you might say okay well these are two different ideas and they seem like two different ideas until we start thinking about a couple of things one Newton's second law and also how you would actually go about measuring mass so how would you actually measure this right over here how would you measure mass because you might say well maybe you just look at this the size of the object but the size by itself doesn't tell you how much stuff there is you could have a very large object that's not very dense but means let's say cotton candy or a hot air balloon and you could have a very small object that's very very dense you could take a lead weight or something even denser a teaspoon of the material from a neutron star incredibly incredibly dense very very high mass so you couldn't just look at the the size or the volume of an object but lucky for us Newton's second law does give us a tool for figuring out the mass of an object Newton's second law tells us that the force that acts on an object is equal to the mass of that object times the acceleration of that object and the acceleration and the force are going to go in the exact same direction or if you want to think only about the magnitudes you can say the magnitude of the force on a on a not on a object is going to be equal to its mass its mass its mass times the magnitude of the acceleration they say well how does this allow me to measure an object's mass well I can apply some force to it I can apply some force a certain magnitude and then I can measure how much that object is accelerated and then I could just solve for MU divide both sides of this equation by a you get F over a is equal to M but what am i measuring so I will actually solve for a mass here I could you know I'll get my proper units of mass depending on what my units of force and acceleration are right over here but what am i implicit ly measuring as well well I'm applying a force on something and I'm seeing how much it's accelerating I'm seeing what is its resistance to accelerating so I'm really trying to also determine its inertia so when you think about mass in this way we now think about this is actually inertial mass inertial inertial mass one way to think about is that the mass is actually quantifying that object's inertia so we can split hairs over the definitions but in this way of viewing mass mass and inertia are really the same thing and it's actually very hard to just directly measure how much stuff or matter there is that's why I put it in quotes right here the more pure definition of what mass even is is or one of the more pure definitions of what mass even is is how resistant is that object to acceleration because especially once you start getting into the subatomic domains the quantum domains the idea of how much stuff there is starts to become very abstract and all we can do is measure how does how does that that entity or that particle how does that respond to force how resistant is that to acceleration and that will and that is essentially what we're describing is mass or inertial mass but you might say wait wait that's not the only way to measure mass you have Newton's law of gravitation I could have some object that has a known mass so let's say this is some object with a known mass let's call it m1 and let's say that there's some other object with an unknown mass let's call it m2 and this is the mass that we are trying to measure and we know that they're going to exert they're going to they're going to pull on each other Newton's law of gravitation and everything we're talking here we're talking about classical mechanics that's the world we're going to deal with we're not going to talk about we're not going to talk general relativity or anything like that right now well we know if we know this mass and if we know the distance between them we know the distance between their center of masses so just like that and if we can measure their respective pulls on each other so we know that if m2 is pulling on m1 with some force so I'll draw that as a vector like this m1 will pull on m2 with an equal and opposite force so a force with the same magnitude but just the opposite direction and so we can measure what that force is we can we know what m1 is we know the distance between them and from that we can figure out what m2 needs to be and from and and when you measure mass when you think about mass in this way you're actually referring to gravitational mass me right this way this right over here is gravitational gravitational gravitational mass now lucky for us it has been verified that these two things these two things are actually measuring the exact same thing that inertial mass is equivalent to gravitational mass so you can debate on the definitions and it might be a little different in different contexts sometimes people want you to think of more in classical terms inertia as resistance to acceleration mass is how much matter there is but essentially they're talking about the same thing mass is a measure of how resistant something is to acceleration or mass is a measure of inertia