In lecture D9, we saw the principle of impulse and momentum applied to particle motion. This principle was of particular importance when the applied forces were functions of time and when interactions between particles occurred over very short times, such as with impact forces. In this lecture, we extend these principles to two dimensional rigid body dynamics. Impulse and Momentum Equations Linear Momentum In lecture D18, we introduced the equations of motion for a two dimensional rigid body. The linear momen- tum for a system of particles is defined

In this lecture, we consider the motion of a 3D rigid body. We shall see that in the general three dimensional case, the angular velocity of the body can change in magnitude as well as in direction, and, as a consequence, the motion is considerably more complicated than that in two dimensions. Rotation About a Fixed Point We consider first the simplified situation in which the 3D body moves in such a way that there is always a point, O, which is fixed. It is clear that, in this case, the path of any point in the rigid body which is at a

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

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 will consider how to transfer from one orbit, or trajectory, to another. One of the assumptions that we shall make is that the velocity changes of the spacecraft, due to the propulsive effects, occur instantaneously. Although it obviously takes some time for the spacecraft to accelerate to the velocity of the new orbit, this assumption is reasonable when the burn time of the rocket is much smaller than the period of the orbit. In such cases, the Av required to do the maneuver is simply the difference between the

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)

DISCOVERy OF THE ROLE OF UBIQUITIN IN PROTEIN DEGRADATION HISTORICAL FACTS Courtesy of Sam Griffiths-Jones. Used with permission Source: \Peptide models for protein beta-sheets hD thesis, University of Nottingham, 2001 8(1975)Ubiquitin was first isolated by Gideon Goldstein and colleagues from the thymus(reason why it was originally thought to be a thymic hormone)

Rip: REGULATED INTRAHENBRANE PROTEOLYSis .Site. spacifie membrae. prote2ses Substratey achivated by protcolytc procassing .. SREBP TF controlling rol metabohis IRE1 Unfolded protein response Notch APP \RoP*: REGULATED. UBiQUiTIN/PROTEASOME DEPENDENT PROCESSING\ type ERAD (ER zciakd dxgradatin) process involving proltoly'c procassing:

Figure 2 in Muratani M, Tansey WP. \How the ubiquitin-proteasome system controls transcription.\ Nat Rev Mol Cell Biol. 2003 Mar; 4(3): 192-201. Regulation of TCR by ubiquitylation of RNA polymerase II. Transcription-coupled repair (TCR)is the mechanism through which mutations in actively transcribed genes are preferentially repaired. a Elongating RNA polymerase II (pol II)