3.10: Kinetic energy
( \newcommand{\kernel}{\mathrm{null}\,}\)
We remind ourselves that we are discussing particles, and that all kinetic energy is translational kinetic energy.
Notation:
- TC = kinetic energy with respect to the centre of mass C.
- T = kinetic energy with respect to the origin O.
T=TC+12M¯v2
Thus:
T=12∑miv2i=12∑mi(v′i+¯v)⋅(v′i+¯v)
=12∑mv′2iׯv∑mv′i+12v−2∑mi.
∴T=TC+12M¯v2.
If ¯v=0,T=TC. (Think about what this means.)
Corollary: For a non-rotating rigid body, TC = 0, and therefore T=12M¯v2
(Think about what this means.)