Αποτελέσματα Αναζήτησης
Calculate the center of mass of a given system. Apply the center of mass concept in two and three dimensions. Calculate the velocity and acceleration of the center of mass.
Find the center of mass of a uniform thin hoop (or ring) of mass \(M\) and radius \(r\). Strategy First, the hoop’s symmetry suggests the center of mass should be at its geometric center.
Suppose that we imagine an object to be made of two pieces, $A$ and $B$ (Fig. 19–1). Then the center of mass of the whole object can be calculated as follows. First, find the center of mass of piece $A$, and then of piece $B$. Also, find the total mass of each piece, $M_A$ and $M_B$.
The center of mass of an object need not lie within the object. There is no dough at the com of a doughnut, and no iron at the com of a horseshoe. SAMPLE PROBLEM 9.1.1 com of three particles Three particles of masses m 1 = 1.2 kg, m 2 = 2.5 kg, and m 3 = 3.4 kg form an equilateral triangle of edge length a = 140 cm.
In the previous modules on “Center of Mass and Translational Motion,” we learned why the concept of center of mass (COM) helps solving mechanics problems involving a rigid body. Here, we will study the rigorous definition of COM and how to determine the location of it.
We will introduce the very important concept of the center of mass of a system of particles and determine the center of mass for both discrete and continuous mass distributions. We will use Newton’s second law to obtain the equations of motion for the center of mass of a system of particles.
For example, imagine supporting a rod or sheet of material at the point where it is perfectly balanced; this will be the body's center of mass. The center of mass may be defined for a collection of discrete masses, or for a continuous body; it may also be defined in one, two, or three dimensions.
