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.
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.
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 $M_B$.
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.
20 Ιουλ 2022 · The center of mass vector, \(\overrightarrow{\mathbf{R}}_{\mathrm{cm}}\), of the two-body system is defined as \[\overrightarrow{\mathbf{R}}_{\mathrm{cm}}=\frac{m_{1} \overrightarrow{\mathbf{r}}_{1}+m_{2} \overrightarrow{\mathbf{r}}_{2}}{m_{1}+m_{2}} \nonumber \]
