Αποτελέσματα Αναζήτησης
Explain the meaning and usefulness of the concept of center of mass. 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 $M_B$.
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.
This example of a uniform rod previews some common features about the process of finding the center of mass of a continuous body. Continuous mass distributions require calculus methods involving an integral over the mass of the object.
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.
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.
