Question

2. Consider Npoint masses. Assume that they Figure 1 and they moves like one kinetic energy is rigidly connected by massless stiff rods as illustrated in are rigid body. Its angular velocity is measured as w. Show that the total 1 T = 1 T =M||VGll2 +TIG where M is the total mass, vG is the velocity of the mass center, and I is the moment of inertia measured at the mass center Hint Start from the sum of kinetics energies: T =-^m; ||Vi||2. . Figure 1

Answer 1

- Sol Let with Rigid body congists masses mi, moving with of many velocitios e particles so that total Kinetic energy is K = { z m (17.7) ->0 If we now de fine a relative velocity of each Particle with respect to center of mass as -N x = Į & mi creare 3¢ mi ca tien). Co tema) = į palm caremoniemrem- Emes + į Eminem where ţ Emine on a Mac or a mome? - Treuslation (im=emi) Kinetic energy of center of mass pem(Emo!- Zero Since velocity of Center of 1 mass with respect to center of į Emit = Ž Emi R ² = 4 w²1 cm 21 - Rotational ( In = Icm= & m: Ri?) - Kinetic energy around the Rotat K= { mol + < Troy w we? C.WJP=62) Hence proved mass is zero Centre of mass . .