# Center of Mass

by Jared Rovny

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00:01 Now we're gonna move to the center of mass.

00:04 The idea of center of mass is just to ask where would an object balance.

00:09 In other words, where could I put my finger or put a string that's holding the object so that the object would be perfectly balanced at that point.

00:16 If I, for example, took an object like this one and hang it from a string, I can draw a dotted line down exactly in the line of the string itself.

00:26 If I then hang the object from a different point maybe from the side I could repeat and also draw a dotted line, the place where this dotted line meet would be the center of mass of the object.

00:36 At this particular point on the object if you balance it perfectly on your finger or another object and be very careful it would stay perfectly balanced, meaning that mass is equally distributed about that point because it is by definition the center of mass.

00:50 The center of mass is important because for any object anything you consider you can find the center of mass of that object including for a person.

00:58 So as a person, grows and ages and changes how they walk and their posture the center of mass of that person can also change where its location is and has a very important ramifications for the mechanics of the body and how the body works and has to come as using its muscle depending on where a person's center of mass is.

01:16 It's also important to notice that the center of mass does not necessarily need to be inside the object itself.

01:22 So for example, if you consider somebody hunch over like this if they're bend like this the center of mass can be actually be residing outside the person, because the center of mass is not talking about our location within the mass, the center of mass is trying to tell you where the mass is equally distributed around and that can again be outside of the object itself.

01:39 Let's do a quick pictorial, representation of center of mass, supposed we have two point objects like this and we're just considering one dimension along the x direction, where x is equal zero and then goes off to the side.

01:54 One mass is much bigger than the other and we could expect just by intuition of the center of mass of the system of two masses, would be somewhere in between but more towards the heavier mass.

02:04 The way to find this mathematically, is to multiply the masses times the position of the objects and then to divide it by the total mass of your system.

02:14 So if you look at the numerator of this expression we have mass 1 times its position plus mass 2 times its position and if we have more masses we would keep going.

02:22 But, if we just lifted it at that way, we would have units of mass times position, and that's not a good location.

02:29 For location we need units of distance, and so we have to divide it by the masses at the end.

02:34 What we're doing here conceptionally, is we're giving each position X1 and X2 etc.

02:41 It's on weight per see we're sort of biasing the center of mass towards heavier objects.

02:46 So in other words, X1 here gets more of a say more of a weight toward its position because it has a large mass located at X1.

02:55 And then at the end of the day again we divide it by the total mass so that we end up with units of just position.

The lecture Center of Mass by Jared Rovny is from the course Force.

### Included Quiz Questions

1. The mass of an object is equally distributed around its center of mass.
2. The mass of an object is strongest at the center of mass.
3. The center of mass is at the geometric middle of an object.
4. The center of mass is always located inside the object itself.
5. The center of mass is at the bottom of a stable arrangement of objects.
1. If an object is placed at x=0, it will still weight the center of mass towards its location as would any other object.
2. If an object is placed at x=0, it will disappear from the equation because its mass will be multiplied by zero. Thus, it will not contribute.
3. An object can never be placed at x=0 because it will contribute less than it otherwise should.
4. If an object is placed at x=0, it will shift the center of mass towards the next mass in the equation.
5. If an object is placed at x=0, the coordinates can be shifted to account for the lack of mass contribution.

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