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Current time:0:00Total duration:6:14

just for kicks let's imagine someone spinning a flaming tennis ball attached to some type of a string or chain that they're spinning it above their head like this and let's say they're spinning it at a constant speed we've already described situations like this maybe not with as much drama as this one but we can visualize the velocity vectors at different points for the ball so at this point let's say the velocity vector will look like this the linear velocity vector just to be super clear so the linear velocity vector might look something like that and it's going to have magnitude V the magnitude of the velocity vector you can also view as its linear speed now a few moments later what is the ball going to be doing well a few moments later the ball might be let's say right over here we don't want to lose the drama it's still flaming we're assuming it's still attached it's still attached to our chain right over here but what would its velocity vector be well we're assuming it has a constant speed a constant linear speed so the magnitude is going to be the same but now it's going to be the direction is going to be tangential to the circular path at that point so our direction has changed now one way to think about this change in direction of velocity it's a little bit counterintuitive at first because when we first think about acceleration we tend to think in terms of change in the magnitude of velocity but changing keeping the magnitude the same but changing the direction still involves an acceleration and at first it's a little counterintuitive the direction of that acceleration but if I were to take this second velocity vector and if I were to shift it over here and if I were to start it at the exact same point it would look something like it would look something like this it would look something like this and actually let me doing this slightly different color so it's a little bit more visible so it would look something like this this and this or they have the same lengths and they're parallel so they are the same vector and so in some amount of time if you want to go from this velocity vector and actually this should be a little bit longer this should look this should look like this it should have the same magnitude as this one so it should look like this so if in some amount of time this and this should have the same magnitude if in some amount of time you go from this velocity vector to this velocity vector your net change in velocity is going radially inward this right over here is your net change this right over here is your net change in velocity and so in other videos we talked about this notion of centripetal acceleration in order to keep something going in this uniform circular motion in order to keep changing the direction of our velocity vector you are accelerating it inward radially inward centripetal acceleration inward acceleration and so at all points in time you have an inward acceleration which we denote the magnitude we usually say is a with a C subscript for centripetal sometimes you'll see an A with an R subscript for radial but in this context we will use centripetal now one question that you might have been wondering this whole time that we talked about centripetal acceleration is Newton's first law might be nagging you Newton's first law tells us that the velocity of an object both its magnitude and its direction will not change unless there's some net force acting on the object and we clearly see here that the direction of our velocity vector is changing so Newton's first law tells us that there must be some net force acting on it and that net force is going to be acting in the same direction as our acceleration and so what we're going to do here is introduce an idea of centripetal force so the centripetal force if it's accelerating the object inwards and the centripetal I guess you say in the inward direction so we have a centripetal force that is causing with that is causing our centripetal acceleration F sub C right every could be that is the magnitude of our centripetal force and the way that they would be connected this comes straight out of Newton's sec this isn't some type of new different type of force this is the same type of forces that we talked about throughout physics we know that our the magnitude of our centripetal force is going to be equal to the mass of our object times the magnitude of our centripetal acceleration you could if you want you could put vectors on top of this you could say something like this and we know but we know the direction of these of the centripetal force and the centripetal acceleration it is inward now what inward means the exact arrow is going to be different at different points but for any position for the ball we know at least conceptually what inward is going to be so this is just to appreciate the idea centripetal acceleration in classical mechanics isn't just going to show up out of nowhere Newton's first law tells us that if something is being accelerated there must be a net force acting on it and if it's being net if it's if it's being accelerated inward in the centripetal direction I guess you could say then the force must also be acting inward and they would just be related by F equals MA which we learn from Newton's second law and to appreciate the intuition for this just remember the last time that you were spinning or rotating a flaming tennis ball attached to a chain above your head in order to do that in order to keep the ball spinning and not just going and veering off in a straight line you had to keep pulling you have to keep pulling inward on your chain so that the flaming tennis ball doesn't go hit a wall and set things on to fire and so what you are providing is that centripetal force to keep that flaming tennis ball in its uniform circular motion