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Current time:0:00Total duration:10:47

Video transcript

let's say we observe some object let's say for the sake of argument it's happening in space and it's travelling in a circular path with the magnitude of its velocity being constant and I want to be very clear here because the magnitude so let me draw it's a velocity vector so that is the length of this arrow is the magnitude of its velocity but I want to be clear in order for it to be traveling in a circular path the direction of its velocity needs to be changing so at this time it might the velocity vector might look like that after a few seconds the velocity vector let me do that in a different color so we can keep track of things after a few seconds the velocity vector might look like this after another few seconds the velocity vector might look like this I'm just sampling from I obviously could have sampled after less time and it would have been right over there but I'm just sampling some times as it travels around the circle after a few more seconds the velocity vector the velocity vector might look something like that and what I want to do is think about what needs to happen what kind of force would have to act and in particular the direction of the force that would have to act on this object in order for its velocity vector to change like this and let's remind ourselves if there was no force acting on this body and this comes straight from Newton's first law of motion then the velocity would not change neither the magnitude nor the direction of the velocity would change there were no force acting on this object it would just continue going on in the direction it was going it wouldn't it wouldn't curve it wouldn't turn the direction of its velocity wasn't changing so let's think about what what the direction of that force would have to be and to do that I'm going to copy and paste these these velocity vectors and we can keep track of what the change in velocity or especially the direction of the change in velocity has to be so let's say copy and let me paste that so that is our first velocity vector let me scroll a little bit to the right so that's our first velocity vector let me copy all of these this is our second one right over here this is our second one let me copy and paste it so I'm just looking at from the point of view what how does the velocity vector change from each of these points in time to the next and then let me get all of these in there so then let me get this green one looks like that so let me copy and let me paste it put it like that and then let me do and I could keep going I could keep drawing velocity vectors around this circle but let me do this orange one right over here so copy and then paste so do just like that so between this purple time and this we do this and we do it in white between this purple time right over here and this and I guess this magenta time and this purple time what was the change in velocity well we can look at that purely from these vectors right here the change in velocity between those two times was that right over there that is our change in velocity so if we were to take this vector this little white vector that I did and said okay what was it what in what direction was the velocity changing when the object was going on this part of the arc well it was roughly if I were to just if I were to just translate that vector right over here it's roughly going in that direction so that is the direction of our change in velocity this triangle is Delta Delta is four change now let's think about the next little time period between this blue or purple period and this green period our change in velocity would look like that change in velocity so while it's traveling along this part of the arc roughly it's the change in velocity if you if we if we draw the vector starting at the object it would look something like this I'm just translating actually do it a little bit it looks something like this I'm just translating this vector this vector to right over here and then I'll just do it one more time and let me do it in this blue color so from this green point in time to this orange point in time and obviously we're just sampling points it's continuously moving and the change in velocity is actually continuously changing but hopefully you're going to see a pattern here so between those two points in time this is our this right here is our this right here is our change in velocity and so if I were to translate that vector right over there it would look something like that change in velocity so what do you see and if I were to if I were to keep drawing more of these change in velocity vectors you would see at this point the change in velocity would have to be going generally in that direction if at this point the change in velocity we have having to go generally in that direction so what do you see what's the pattern for any point along this circular curve what's the pattern well the change in velocity is first of all it is perpendicular to the direction of the velocity itself and we haven't proved it but it at least looks like it it looks like this is perpendicular and even more interesting it looks like it's seeking the center the change in velocity is constantly going in the direction of the center of our circle the center of our circle and we know from Newton's first law that if the if the velocity is changing it the magnitude could stay the same but if the velocity is changing in any way either the magnitude or the direction or both there must be a net force acting on the object and the net force is acting in the direction of the acceleration which is causing the change in velocity so the force must be acting in the same direction as this change in velocity so in order to make this object go in this circular path there must be some force some force causing kind of pulling the object towards the center and a force that is perpendicular to its direction of motion and this force is called the centripetal force centripetal centripetal not to be confused with centrifugal force very different centripetal force Sentra you might recognize that reached the center and then petal is comes from its seeking the center so let me write that it is center it is center it is center seeking and so this centripetal force something is pulling on this object towards the center that causes it to go in this circular motion and oil and that's that inward pulling causes inward acceleration so that's centripetal force a centripetal force causing causing centripetal acceleration acceleration which causes the object to go to words the center the whole point why I did this is it at least it wasn't intuitive to me that if you have this object going in a circle that the change in velocity the acceleration the force acting on this object would actually have to be Center or it would have to be towards the center and the whole reason why I drew these vectors and then translated them over here and then drew these change in velocity vectors is to show you that the change in velocity is actually towards the center of this body now or towards the center of the circle now with that out of the way you might say well where does this happen in everyday life or actually I guess in reality in some way shape or form and the most typical example of this and this is something that I think most of us have done when we work it is if you had a yo-yo if you have a yo-yo we've got my best attempt to draw a yo-yo if you have a yo-yo and if you whip it around on a string if you whip it around on a string you know that the yo-yo goes in a circular it goes it goes in a circle it goes in a circle even though its speed might be constant or another way of thinking about to be the magnitude of its velocity might be constant we know that the direction of its velocity is constantly changing its going in a circle and what's causing it to go in a circle is your hand right over here pulling on this string and providing tension into that string so there's a force the centripetal force in this yo-yo example is the tension in the string that's constantly pulling on the yo-yo towards the center and that's why that yo-yo goes in a circle another example that you are probably somewhat familiar with or at least have heard about is if you have if you have something in orbit around a planet so let's say that this is Earth right here this is Earth right here and you have some type of a you have some type of a satellite draw a satellite you have some type of a satellite that is in orbit that is in orbit around Earth that satellite that satellite has some velocity at any given moment in time but what's keeping it from not flying out into space and keeping it going in a circle is the force of gravity so in the example of in the example of a satellite or actually anything in orbit even the moon in orbit around the earth the thing that's keeping it in orbit as opposed to flying out into space is the centripetal force of Earth's gravity now another example and this is probably the most everyday example because we do it all the time if you imagine a car traveling around a racetrack so let me draw a racetrack right up around here if I have a racetrack and I just before I tell you the answer I'll have you think about it so let me draw my best attempt at a racetrack so let me just draw a circular I'm not going to even bank the racetrack so let's look at the racetrack from above so if I have a car on a racetrack I want you to and pause this before I tell it to you because I think it's an interesting thing to think about because it seems like a very obvious thing that's happening we've all experienced we've all taken turns in cars so that we're looking at the top of a car that's its tires we're looking at the top of a car and when you see a car going at a constant speed so on the speedometer it might just say whatever 60 miles an hour or 40 miles an hour whatever the constant speed but it's traveling in a circle it's traveling in a circle so what is keeping what is the centripetal force in that example there's there's no obvious string being pulled on the car towards the center there's no some magical gravity pulling it towards the center of the circle there's obviously gravity pulling it down towards the ground but nothing pulling it to the side like this so what's keeping this car what's causing this car to go in the circle as opposed to going straight and I encourage you to pause it right now before I tell you the answer so assuming you've now unpause it I will now tell you the answer the thing that's keeping it going in the circle is actually the force of friction it's actually it's actually the force between the the the that resists movement to the to the side between the tires and the road and a good example of that is if you were to remove the friction of the road if you were to make the car drive on oil or on ice or if you were to if you were to shave the treads of the tire for some type of a plastic tire or something then a car would not be able to do this so it's actually the force of friction in this example so I encourage you to think about that