In this exercise, we will use the principle of angular momentum to eventually derive the moment of inertia integral. For each case, ?nd the angular momentum HO of the system and match your result with the formula
Ho = Io*w
i.e. pull out the term ! and recognize that Io is whatever you have multiplying w.
(a) Show that the moment of inertia of a particle of mass m rotating about some point O at a distance R with angular speed w is
Io = m*R2
(b) Show that the moment of inertia of n particles, each of mass (1/n)*m rotating about some point O at a distance R with the same angular speed is
Io = m*R2