Viewing g as the value of Earth's gravitational field near the surface

what I want to do in this video is think about the two different ways of interpreting lowercase G which as we've talked about before many textbooks will give you as either 9.81 m/s^2 downward or towards the center Earth's center or sometimes it's given with a negative quantity that signifies the direction it was essentially downwards negative 9.81 m/s^2 and probably the most typical way to interpret this value as the acceleration so let me write acceleration due to gravity due to gravity near near Earth's surface near Earth's surface for an object in freefall and this is what we're going to focus on in this video for an object object in freefall and the reason why I'm stressing this last part is because imagine or we know of many objects that are near the surface of the earth that are not in freefall for example I am near the surface of the earth right now and I am NOT in freefall what's happening to me right now is I'm sitting in a chair and so this is my chair draw a little stick drawing of my chair and this is me this is me and let's just say that chair supporting all my weight so my legs are flying in the air so this is me and so what's happening right now if I were in freefall I would be accelerating towards the center of the earth at 9.81 m/s^2 but what's happening is is all of the force due to gravity so all of the force due to gravity is being completely offset by the normal force from the surface of the chair onto my onto my pants and so so this is normal force and all right make them both as vectors I'll make them both as vectors so the net force so the net force in my situation the net force is equal to zero especially in this vertical direction and because the net force is equal zero I am not accelerating towards the center of the earth I am not in freefall and because this nine point eight one eight one meters per second squared still seems relevant to my situation and I'll talk about that a second but I'm not an object in freefall another way to interpret this is not as the acceleration due to gravity near Earth's surface for an object in freefall although it is that may be a more general way to interpret this as the gravitational or Earth's gravitational field or it's really the average acceleration or the average because it actually changes slightly throughout the surface of the earth but another way to view this as the average gravitational field at Earth's surface let me write that way in pink so the average gravitational field and we'll talk about what a field means in the physics context in a second field the average gravitational field at at Earth's surface and this is a little bit more of an abstract thing we'll talk about that in a second but it does help us think about how G is related to this scenario where I am NOT an object in freefall a field when you think of it in the physics context slightly more abstract notion when you start think about in the mathematics context but in the physics context a field is just something that Associates a quantity with every point in space so this is just a quantity quantity with every point point in space and it can actually be a scalar quantity in which case we would call it a scalar field in which case would just be a value or it could be a vector quantity which would be a magnitude and a direction associated with every point in space in which case you are dealing with a vector field and the reason why this is called a field is because at near Earth's surface near Earth's surface if you give me a mass so for example I don't actually I don't know what my mass is in kilograms but if you're a near Earth surface and you give me a mass so let's say that mass right over there is 10 kilograms you can use G to figure out the actual force on that of gravity on that object at that point in at that point in space so for example if this has a mass I mean this has a mass of 10 kilograms then we know in this right over here is the surface of the earth so that's the center of the earth so it actually Associates a vector quantity whose magnitude so it's Direction is towards the center of the earth and the magnitude of this vector quantity is going to be the mass times times G times and you could take since we're already specifying the direction we could say 9.81 m/s^2 towards the center of the earth and so in this situation it would be 10 kilograms 10 kilograms times 9.81 9.81 m/s^2 which is 98 98.1 and even this i've rounded a little bit so it's it's actually approximate number 98.1 kilogram meters per second squared or which is also a unit which is the unit of force or 98.1 newtons and this thing might not be in freefall and so this is this is why it becomes why G is relevant even in a situation where the object isn't in freefall G has given us the force per unit mass the force per mass of of groove of gravity on an object near the surface of the earth so this let me another way to think about it so this is the average gravitational field and what it's giving is what it's giving is force force per mass so you give me a mass near Earth's surface whether it's an object in freefall or not you multiply that mass times G because it's giving you force per mass and it will give you Earth's gravity it'll give you the force of gravity acting on that object near the surface of the earth whether or not it's in freefall so I just want to make this little distinction because although G tends to be referred to this way right over here sometimes you might encounter a stickler who says oh no no no no but G is relevant even when an object is not in freefall you obviously can't say that my acceleration when I'm sitting in my chair is 9.81 m/s^2 towards the center of the earth I am NOT accelerating towards the center of the earth and so they'll say oh no no no it's you you can't just call this you can't just call this acceleration it is true - it is the acceleration when an object is in free fall when near the surface of the earth if you don't have really air resistance if gret if the net force really is the force of gravity then this really would be the object's acceleration but it becomes relevant and we know most objects that we know if aren't in freefall obviously an object in freefall doesn't stay in freefall for long it eventually hits something but we know that now G is actually relevant to all objects it tells us the force per mass as tempting to call it always acceleration because the units are acceleration but even when you talk about it in terms of the gravitational field is still the same quantity it still has it still has the exact same units the same magnitude and the same direction it's just a different way of viewing it here acceleration for an object in freefall here something to multiply by mass to figure out the force due to gravity