In this lecture, we will particularize the conservation principles presented in the previous lecture to the case in which the system of particles considered is a 2D rigid body. Mass Moment of Inertia In the previous lecture, we established that the angular momentum of a system of particles relative to the center of mass, G, was
A pendulum is a rigid body suspended from a fixed point (hinge) which is offset with respect to the body's center of mass. If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum. Pendulums have played an important role in the history of dynamics. Galileo identified the pendulum as the first example of synchronous motion, which led to the first successful clock developed
In this lecture, we will derive expressions for the angular momentum and kinetic energy of a 3D rigid body. We shall see that this introduces the concept of the Inertia Tensor. Angular Momentum We start form the expression of the angular momentum of a system of particles about the center of mass
D244BD RIGID BODY DYNAMICS KINETIC EWEGY In echure we derwed am kinenc a susem u dm T= Fere ts the velouty relanve to G. for a nald body we ca wate Uing the vechor nidontklyAxB=Ax
In this lecture, we consider the problem of a body in which the mass of the body changes during the motion, that is, m is a function of t, i.e. m(t). Although there are many cases for which this particular model is applicable, one of obvious importance to us are rockets. We shall see that a significant fraction of the mass of a rocket is the fuel, which is expelled during flight at a high velocity and thus, provides the propulsive force for the rocket
Lecture D33: Forced Vibration Fosinwt m Spring Force Fs =-kx, k>0 Dashpot Fd =-ci, c>0 Forcing Fext Fo sin wt Newton's Second Law (mix =CF) mx+cx+kx= Fo sin wt =k/m,=c/(2mwn)
