So, in a sense, it can be easier to think about the total energy of a system and the vibrational portion is the bit that's left over. In terms of separating the energy into different terms, you are only interested in the kinetic energy portion of this energy, but it is hard to separate from the potential unless you have a known set of conditions (e.g., precisely how compressed the spring is at a given time/location). Think about the spring-mass oscillations from previous notes. It's clear there can be energy due to vibration even if the center of mass doesn't move. That is, the total energy due to vibrations is due to the potential energy associated with the interaction causing the vibrations and the kinetic energy of the vibrations themselves. You read about the energy associated with vibrations earlier, but this energy contained both potential and kinetic terms. The thermal energy of the system is the average kinetic energy of the systems constituent particles due to their motion. Separating the Total Kinetic Energy in a Multi-Particle System Luckily, we can separate the motion of the center of mass of the baton from the motion around the center of mass, making this energy calculation simpler.

Adding up all the kinetic energies of the atoms here is a real pain. This is another form of the relative velocity motion that you read about earlier. Relative to the fixed frame of the ground, the atom on the right, at this instant, is moving faster than the atom on the left.

At this instant, the atom on the right is moving up as the baton rotates. 1) In this case, you can still add up the velocities of each atom, but now you have taken into account the translational velocity of the whole baton.Д¬onsider a pair of atoms that are the same distance from the center of the baton (red circles in the figure to the right). The kinetic energy of the baton has increased because the baton is both translating and rotating. The whole baton is moving up with a known speed. Now, consider that this baton is now tossed into the air while it twirls. The kinetic energy of atoms on either side of the center (but at the same distance from it) has the same kinetic energy because they move at the same speed. This is fairly simple (but painful) to do. You could add up all the individual velocities of the atoms to get the total kinetic energy of the baton. As the baton is twirled, each atom in the baton moves in a circle at a speed that depends on how far the atom is from the center of the baton. Atoms (red circles) on either side of the center of a twirled and tossed baton have different speeds.Д¬onsider a baton that is being twirled in a circle in someone's hand.

Total kinetic energy of particles