Center of mass?

Question

Of what use is knowing the center of mass of an object when making calculations?

Answer 1

knowing where the centre of mass is great for calculations using torque... torque = distance(from centre of mass) * force

Answer 2

The center of mass calculations is very useful for the NASA people when they are launching rockets and cargo from a rocket, like a probe. Another useful application is determining the recoil of a gun, or any other fire weapon, when one shoots with it. In fact, it is useful for any process in which an object turns itself in its counterparts and the dimensions of its counterparts are comparable with the initial object.

You see, when an object blows up, or just turns itself in its counterparts, and it is moving with a constant velocity, the center of mass of that object keeps moving with the same velocity, even if the counterparts don't preserve the movement before the explosion and even if the center of mass doesn't have a physical support (think at the center of mass of a ring or of a triangle).

In this case, one may control the direction of the bullet, for instance, when he/she shoots. When one fires a gun, because of the differences in masses between the gun and the bullet, the bullet goes out with a high velocity, while the gun has a small velocity, such that the M*V=m*v, where the capitals are the mass (M) and the velocity (V) of the gun and the small letters are the mass (m) and the velocity (v) of the bullet. That is why one can still hold a gun in his hand without being thrown at several metres away from the place he/she has fired. And the center of mass remains still in this case, as the gun wasn't walking around when it was fired.

Hope this helps.

Answer 3

The center of mass (CM) is a virtual point within a body where the physical effects of all mass for that body reside. When the mass density of a body is uniform throughout that body and that body has a symmetric shape (like a ball), CM can be found in the geometric center of that body.

But when the mass density is nonuniform or it is not symmetric, or both, CM is often nowhere close to the geometric center. For example, if you have a big letter C, made up of iron, the CM would likely fall outside the C, somewhere back from the opening in the letter. CM can frequently be found through triple integration of the body's mass density if there is a good, continuous set of mathematical relationships that can be integrated.

CM is useful because there are a number of mass related equations in classical physics that can use the fact that all mass of a body can be represented as being located at that center. For example, F = GmM/r^2 is the force between two masses (m and M) due to gravity. r is the distance between the two masses measured between the CM of each one. Also, a moment L = Fd; where F is a force applied to a body some distance d from that body's CM.

Even F = ma uses the CM, because the force F is applied to the CM of the body with mass m to work most, if not all, classical physics problems. Similarly, weight W = mg is represented as a force passing through the center of mass on a body.

Bottom line, CM is very useful for solving a wide variety of force related problems.

Answer 4

Using the center of mass makes it much much easier to calculate the gravitational force between two objects (F = GMm/(r^2)). The alternative is to integrate the forces over all the infinitesimal elements of mass in both objects, however both yield the same total force.

Answer 5

centre of mass is that point of an object which govern the movement of the whole body. instead of taking account of the whole object we take a small point of the object >centre of mass because it easier to calculate for a point mass rather to calculate for a whole body.The result will be same. specially in rotation mechanic we take into account of centre of mass because in rotationl motion every particle is continously changing direction so it difficult to make a calculation for the whole than calculating for centre of mass.

Answer 6

Using the centre of mass you can treat the object as a particle whose mass is that of the object

Answer 7

It can be shown that ANY motion of ANY object can be reduced to:

1) linear motion of the center of mass(F=ma)
2) rotational motion about the center of mass.

Answer 8

The centre of mass it where the object is in balance
i.e. if you can suspend it from this point then you can move the object in any direction and it stay where you place it.

Answer 9

I'm doing a civil engineering degree and we use it quite a bit for such things as buoyancy. and for when doing calculations relating to buildings. i would do an example but i hate calculating it.