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.
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 $M_B$.
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. If we define our coordinate system such that the origin is located at the center of the hoop, the integral should evaluate to zero.
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.
OpenStax. Learning Objectives. 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.
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.
28 Μαρ 2024 · The center of mass is that position in a system that is described by Newton’s Second Law when it is applied to the system as a whole. The center of mass can be thought of as an average position for the system (it is the average of the positions of the particles in the system, weighted by their mass).
