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Main content
Current time:0:00Total duration:5:05

Identifying centripetal force for ball on string

CHA‑4.A (EU)
CHA‑4.A.2 (EK)
CHA‑4.A.2.1 (LO)
INT‑3.B (EU)
INT‑3.B.2 (EK)
INT‑3.B.2.1 (LO)

Video transcript

what we're going to do in this video is try to look at as many scenarios as we can where an object is exhibiting uniform circular motion it's traveling around in a circle at a constant speed and what we want to do is think about why is staying on the circle what centripetal force is keeping the object from just going off in a straight line so in this first scenario I have some type of a wheel maybe a ball attached to a string that it's attached to a peg at the center of the table and this wheel is moving in a circle at a constant speed so it's moving in this circle at a constant speed so pause this video think about all of the forces that are acting on this wheel and which of those forces or maybe some combination of those forces that are actually acting as the centripetal force that are keeping the wheel on the circle all right now let's work through this together so there's a couple of forces that aren't impacting the wheels staying on the circle so much but they're there for example you're definitely gonna have the force of gravity we're assuming we're dealing with this wheel on a planet so that would will denote its magnitude as capital F sub G and then this is its direction with this orange arrow so that's the force of gravity and the reason why the the wheel is not accelerating downward is that we have that table there and so the table is exerting a normal force on the wheel that counteracts the gravitational force so the magnitude there would be the force the normal force and these are going to be the same magnitude they're just going to be in different directions and so let me see if I can draw this arrow a little bit taller but what else is going on well as you can imagine if this string wasn't here the wheel really would go off at a straight line and eventually fall off of the table and so the string is providing some inward force that keeps this the the wheel going in a circle and that inward force that pulling force we would consider that to be the tension force so I'll just draw it like that and it's magnitude is F sub T and in this situation it is providing that inward force so that is the centripetal force so we could say the magnitude of the tension the tension force the pulling force is going to be equal to the centripetal force and in this case they are actually the exact same vector so I can even write it I can even write it like this this is the centripetal force vector it's the tension in that rope that keeps us going in a circle let's do another example so this one is similar but I have a few more dimensions going on here this is a classic example from physics I have a string attached to the ceiling and I have some type of a ball or a pendulum and it's swinging in a circular in a circular motion right over here at a constant speed so the center of its circle would be right around there so once again pause this video think about all of the forces on that ball and we're not going to talk too much about air resistance let's assume that these are in vacuum chambers for now and then think about which of those forces is providing the centripetal force well just like in the last video there's definitely some force of gravity so you have that vector right over there and so it's magnitude is F sub G and you also have the string holding up the ball and so you're going to have it's pulling force on so this would be the magnitude here would be F sub T this is the tension force but what's counteracting the gravity and what's keeping us going in a circle well in this situation we can think about the different components of the tension because this is going off at an angle so if we were break down that vector in the vertical direction so if we take the vertical component or the Y component of the tension force it would look something like this we could call that F T Y for the Y component this would be its magnitude and that is what is counteracting the gravity Y the ball is not accelerating downwards and if we think about the X of the tension that would be this right over here this is the X component of the tension just to be clear where I'm getting this from so this would be F tension in the X direction that would be its magnitude and that is what is providing the centripetal force or that is the centripetal force so in this in this situation the component of our tension in the X direction and let me just denote that as a vector that is our that is our centripetal force that's what keeps the ball from just going straight off in a direction like that