Translational, Rotational and Vibrational Energy: Difference between revisions
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Because the translational kinetic energy is associated to the movement of the center of mass of the object, it is important to know how to calculate the location of the center of mass. | Because the translational kinetic energy is associated to the movement of the center of mass of the object, it is important to know how to calculate the location of the center of mass. | ||
<math> r_{CM} = \cfrac{m_1r_1 + m_2r_2+m_3r_3 + ...}{ | <math> r_{CM} = \cfrac{m_1r_1 + m_2r_2+m_3r_3 + ...}{total_mass} </math> | ||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 16:36, 27 November 2015
Main Idea
In many cases, analyzing the kinetic energy of an object is in fact more difficult than just applying the formula [math]\displaystyle{ K = \cfrac{1}{2}mv^2 }[/math]. When you throw a ball, for example, the ball is traveling through the air, but will also rotate around its own axis. When analyzing more complicated movements like this one, it is necessary to break kinetic energy into different parts and analyze each one separately.
The kinetic energy associated to the movement of the center of mass of the object is called the translational kinetic energy. In terms of the example above, this would be the kinetic energy of the movement of the center of mass of the ball through the air.
The kinetic energy associated to the rotation or vibration of the atoms of the object around its center or axis is called the relative kinetic energy. This kinetic energy is the energy of the ball rotating on its own axis. If this is difficult to visualize, think about how an american football rotates about its center axis when you throw it correctly.
A Mathematical Model
As we just saw, kinetic energy can be divided into two energies: translational kinetic energy and rotational kinetic energy. Therefore, the total kinetic energy of a system is equal to the sum of those two kinetic energies:
[math]\displaystyle{ K_{total} = K_{translational} + K_{relative} }[/math]
The relative kinetic energy term can itself be divided into two other terms. The energy of the atoms of the object relative to its center or axis can either be rotational (this is the case of the football thrown in the air) or vibrational. Therefore, we have:
[math]\displaystyle{ K_{total} = K_{translational} + K_{relative} = K_{translational} + K_{rotational} + K_{vibrational} }[/math]
Because the translational kinetic energy is associated to the movement of the center of mass of the object, it is important to know how to calculate the location of the center of mass.
[math]\displaystyle{ r_{CM} = \cfrac{m_1r_1 + m_2r_2+m_3r_3 + ...}{total_mass} }[/math]
A Computational Model
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