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.
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.
The concept of the center of mass is that of an average of the masses factored by their distances from a reference point. In one plane, that is like the balancing of a seesaw about a pivot point with respect to the torques produced.
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.
