2: Rotational Inertia Let's shift our focus from the description of particle dynamics to rigid body dynamics. Rigid bodies are non-deformable masses composed of an infinite number of particles. (a) Consider the following system, where we have particles 0,1,2,...,n, each of mass m/(n+ 1). The ith particle is at a distance il/nfrom the origin, and particle 0 is position at (x,y) = (0,0). 6 The entire system spins around the origin together with an angle . Calculate ri() = [xi(),yi()]T, the position of the ith particle when the system is at angle . Then, for d dt = , show that the time derivative of ri is calculated: il ri = n sin cos (1) (b) Prove the following formula by induction on n, where n1: n 1 i2 = i=0 n(n+ 1)(2n