If we extend this treatment to the **kinetic energy** , we also
obtain an interesting statement:

(4.38) |

(4.39) |

(4.40) |

(4.41) |

We thus see that the total kinetic energy in the lab frame is the sum
of the kinetic energy of all the particles in the CM frame **plus**
the kinetic energy of the CM frame itself (viewed as single
``object''). To put it another way, the kinetic energy of a baseball
flying through the air is the kinetic energy of the ``baseball
itself'' (the entire system viewed as a particle) plus the kinetic
energy of all the particles that make up the baseball measured in the
CM frame of the baseball itself. This is comprised of **rotational
kinetic energy** (which we will shortly treat) plus all the general
vibrational (atomic) kinetic energy is what we would call **heat**.

We see that we can indeed break up big systems into smaller systems and vice versa!