3.30 ** Consider a rigid body rotating with angular velocity @ about a fixed axis. (You could think of a door rotating about the axis defined by its hinges.) Take the axis of rotation to be the z axis and use cylindrical polar coordinates Pa, Pa, Za to specify the positions of the particles a = 1, ..., N that make up the body. (a) Show that the velocity of the particle a is pow in the p direction. (b) Hence show that the z component of the angular momentum &, of particle o is map w. (c) Show that the z component L2 of the total angular momentum can be written as L. = Iw where I is the moment of inertia (for the axis in question), N 1 = >mala (3.31)