Search results
Results from the WOW.Com Content Network
The experimental determination of a body's center of mass makes use of gravity forces on the body and is based on the fact that the center of mass is the same as the center of gravity in the parallel gravity field near the earth's surface. The center of mass of a body with an axis of symmetry and constant density must lie on this axis.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
where G is the gravitational constant and m is the mass of the body. As long as the total force is nonzero, this equation has a unique solution, and it satisfies the torque requirement. [12] A convenient feature of this definition is that if the body is itself spherically symmetric, then r cg lies at its center of mass.
The mass μ of the one equivalent body equals the reduced mass of the two original bodies, and its position r equals the difference of their positions. Such approximations are unnecessary, however. Newton's laws of motion allow any classical two-body problem to be converted into a corresponding exact one-body problem. [6]
Because all of the mass is located at the same angle with respect to the x-axis, and the distance between the points on the ring is the same distance as before, the gravitational field in the x-direction at point due to the ring is the same as a point mass located at a point units above the y-axis: = (+) /
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance r 0 from the center of the mass distribution: [13] The portion of the mass that is located at radii r < r 0 causes the same force at the radius r 0 as if all of the mass enclosed within a sphere of radius r 0 ...