B a a

N 2 ri Gm2

If rj were the distance of particle i from some axis, then I would be the moment of inertia about that axis. However, an axis is a line, and rj is measured from a point (the origin). Therefore, I is a quantity similar to, but not the same as, the familiar moment of inertia. (For most normal shaped objects it has a numerical value close to the moment of inertia.) We also set the total kinetic energy K equal to the sum of the kinetic energies of the individual particles, i? j

where we have also used the fact that | rjj | = | rjj |. This procedure actually allows for a simplification. To see this, we first multiply out the numerator on the right-hand side to obtain

0 0

Post a comment