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

So far we have used Newton's second law= ma to establish the instantaneous relation between the sum of the forces acting on a particle and the acceleration of that particle. Once the acceleration is known,the velocity (or position) is obtained by integrating the expression of the acceleration (or velocity). There are two situations in which the cumulative effects of unbalanced forces acting on a particle are of interest to us. These involve:

We have seen that the work done by a force F on a particle is given by dw =. dr. If the work done by F, when the particle moves from any position TI to any position T2, can be expressed as, W12=fdr=-(V(r2)-V(1)=V-v2, (1) then we say that the force is conservative. In the above expression, the scalar

例题2-5求例题2-4中所示薄壁圆环在内压力 b p=2MPa作用下的径向应变和圆环直径的改变量。 已知材料的弹性模量E=210GPa p 解:在例题2-4中已经求出圆环在任一横截面 上的正应力=40MPa,若正应力不超过材料的比 例极限,则可按公式(2-6)算出沿正应力方向 (a) (即沿圆周方向)的线应变为

1. Carbohydrates are aldehyde or ketone compounds with multiple hydroxyl groups or substances that can yield such compounds on hydrolysis(p. 293) 1.1 Carbohydrates are the most abundant biomolecules on earth and have multiple roles in all forms of life. 1.1.1 Carbohydrates serve as energy stores (e.g., starch in plants, glycogen in animals), fuels (e.g., glucose), and metabolic intermediates (e.., ATP, many coenzymes)

1. Cells need energy to do all their work To generate and maintain its highly ordered structure (biosynthesis of macromolecules). To generate all kinds of movement. To generate concentration and electrical gradients

process can occur spontaneously is that the entropy changes of chemical reactions are not readily measured. Furthermore, the criterion of sponta- neity given in equation 2 requires that both the entropy change of the surroundings and that of the system of interest be known. These difficul- ties are obviated by using different thermodynar function called the free energy, which is denoted by the symbol G (or F, in the older literature)

Integral Kinetic Energy Equation Idea: Integrate BL flow in y, to \wash out\details in u() profile. Converts PDEs in, y into ODE in T

Applications of Porous Materials Catalys Molecular sIeves Biomedical Application membranes Energy storage http://nano.materials.drexel.edu Degree of Porosity

§14-4 Damped Vibration& Forced Vibration Resonance 阻尼振动 受迫振动 共振 §14-5 Superposition of two SHM with same Frequency in same Direction 同方向同頻率的简谐振动的合成 §14-6 Superposition of two Perpendicular SHM 相互垂直的简谐振动的合成 §14-3 The Energy of SHM 简谐振动的能量 §14-2 Amplitude Period Frequency & Phase 简谐振动的振幅, 周期，頻率和位相 §14-1 Simple Harmonic Motion (SHM) 简谐振动