Center of Mass

hi it's mr. Andersen and this is ap physics essentials video 95 it's on the center of mass I want you to take a look at this tire for a second and I'm going to apply a force to it you can see the motion is fairly regular and the reason why is that the center of mass is right in the middle of that tire and it's rotating around that center of mass now let me apply a force to a hammer and you'll see that the motion is not as uniform it's tricky to our eyes and the reason why is the center of mass i

s off-center what I'm going to do though is keep the center of mass where it is and then I'm going to rotate that hammer and you'll see that the center of mass stays where it is it's just the motion of that object above and below the center of mass that fools your brain now let me show you a system so this is a Saturn 5 rocket it's made up of a number of different stages and so where would you say the center of mass is the average mass well it's maybe somewhere like that what do you think would

happen to the center of mass if I were to break this rocket apart into its two stages at this point well it will stay in the same location and so if we don't have an external force acting on the system the center of mass stays where it is even though that might be rotational motion as we break those stages apart the centre of mass remains where it is and so any system is going to have a center of mass and that center of mass is made up of all the objects within the system and what's neat about p

hysics according to Newton's 2nd law is if we don't apply a net external force then there's going to be constant velocity in other words we're not going to have acceleration in that object it'll either remains still the center of mass or it's going to move with a constant velocity and so how do you figure out where the center of mass is well a good place to get started is with a simulation and this is center of mass builder from simbucket what you can do is you can click on the screen and it sta

rts to make mass it will then show you where the center of mass is so you can see if I make a uniform mass center masses right in the middle what happens if I add another uniform mass in the x-direction it's right between the two what if I move in the I direction you can see that it's going to be the average of that as well so the center of mass doesn't have to be within a specific object what's neat is you can use the hang test in physics so if we simply hang this object if we let it settle out

the vertical line through that hanging point is going to go right through the center of mass so you can calculate the center of mass experimentally and I'll show you how to use an equation to do it a little bit later in the video and so if we apply a force to an object we can get what looks like irregular motion in this hammer but since we've applied a force we know that we're going to have constant velocity and so if I mark where that center of mass is slow it down watch what happens we're goi

ng to have constant velocity and that movement above and below that center of mass is confusing to our brain and so let me show you how this works with a little video I've got two pieces of ice that are connected together with the spring I'm going to apply a force to one and they're going to slide across the ice and so we get this caterpillar like motion so to our brain it looks like we're having acceleration and deceleration but what I want you to do is get involved so I want you to hold your f

inger on the screen where the center of mass is as I play this video where would that center of mass be it's going to be on the spring right between those two blocks of ice and so what you're going to try to do is as I play the video keep your finger between the objects on the spring and so let's do that so you should be tracing it out keep your finger between the blocks and you should find that as you trace it you're showing movement from left to right with constant velocity it's slowing down a

t the end a little bit now let's try a little harder one we've got a force on both of these bricks on either side so again what you're trying to do is hold your finger in between those two bricks on the spring itself so let me play this video and I'm doing this as well so what I'm finding is it's not moving as quickly but it's still moving with constant velocity from left to right and we could do even a complex system like this we have four objects that are connected together with Springs so try

to hold your finger where the center of mass is that's going to be between all four of these objects and if you do that it's hard to kind of keep it in between all four but your brain is pretty good at this again what am i finding there's crazy motion on the screen but my finger is moving across with constant velocity and that's because there's no external force and so we could look at a rocket as a rocket flies through the sky it takes a parabolic path like that so we could trace it out and wo

uld look like that but let's say we're going to take that same rocket and it were to fly through the sky but halfway through it were to break apart into its two different parts so it looks odd in other words that motion looks odd as it breaks apart but if we were to plot the center of the mass it would follow the same parabolic path that that rocket by itself and that's because we have no external force and so what's neat about the center of mass is you can take systems that are incredibly compl

ex and if we just figure out where the center of mass is it makes solving that problem much easier so as you move into ap physics - you'll have to calculate where that center of mass is and so if we have this object right here so we have two masses that are connected with a bar but let's say there's no mass in that bar here's the formula that shows you how to calculate where the center of mass is and what you do is really find the point where you could balance that object on that point and so we

set up an arbitrary distance a distance away in the X from our object and we'll call that X cm that's going to be the center of mass we then set up our two distances this is going to be x1 it's the distance to the center of mass of mass 1 and then X 2 is the distance to the center of mass of mass 2 so our formula all you do is simply multiply mass 1 times X 1 so it'd be this mass times that X plus this mass times that X and then you're dividing the whole thing by the sum of the two masses in ot

her words mass 1 and mass 2 so if I give you some a problem you could pause the video at this point and try to solve it but I'll show you how to work this one out and so what you would do is you would simply multiply mass 1 which is 1 kilogram times the distance which is 2 meters plus mass 2 which is 2 kilograms times the distance of 5 meters and then you divide it by 1 plus 2 kilograms or 3 kilograms so if we set up it looks like that and you should get a distance of 4 meters in other words X c

m is going to be 4 meters from here and so it would be 2 meters from mass 1 and be 1 meter from mass 2 that's a pretty easy problem but if you could throw in different values then you're going to get a harder problem what if I throw in another mass like this how would you solve it now we have three masses and they're moving in the x axis all we do is simply add this mass 3 times X 3 where X 3 is the distance to the center of mass of mass 3 and then we're going to divide by the sum of all three m

asses and so solving it you could have you know twelve masses it's pretty easy to figure out where that center of mass is what if I were to turn it like this instead of going in the X it we're also to go in the Y well how would you do this first of all we would have to get the x coordinate of the center of mass so we're going to use this formula down here you would then choose an arbitrary distance in the Y and then you're going to use the same equation but this time instead of figuring out how

far we're going in the X you'd also figure out how far we're going in the Y now I know my x coordinate my y coordinate and we could even move into the Z to figure out where that center of mass is remember if we don't apply a force to it it's going to have constant velocity and then as you move into ap physics too you have to be able to calculate in one and two dimensions where that center of mass is so I hope that made sense and I hope that was helpful