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)

Lecture D32: Damped Free Vibration Spring-Dashpot-Mass System k Spring Force Fs =-kx, k>0 Dashpot Fd =-cx, c>0 Newton's Second Law (mx =EF) mx +cx+kx (Define)Natural Frequency wn=k/m,and

When the only force acting on a particle is always directed to- wards a fixed point, the motion is called central force motion. This type of motion is particularly relevant when studying the orbital movement of planets and satellites. The laws which gov- ern this motion were first postulated by Kepler and deduced from observation. In this lecture, we will see that these laws are a con- sequence of Newton's second law. An understanding of central

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

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

In this lecture we will look at some applications of Newton's second law, expressed in the different coordinate systems that were introduced in lectures D3-D5. Recall that Newton's second law F=ma, (1) is a vector equation which is valid for inertial observers. In general, we will be interested in determining the motion of a particle given

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

AutoCAD是由美国Autodesk公司开发的通用计算机辅助设计(Computer Aided Design，CAD)软件，具有易于掌握、使用方便、体系结构开放等优点， 能够绘制二维图形与三维图形、标注尺寸、渲染图形以及打印输出图纸，目前 已广泛应用于机械、建筑、电子、航天、造船、石油化工、土木工程、冶金、 地质、气象、纺织、轻工、商业等领域

AutoCAD是由美国Autodesk公司开发的通用计算机辅助设计(Computer Aided Design，CAD)软件，具有易于掌握、使用方便、体系结构开放等优点， 能够绘制二维图形与三维图形、标注尺寸、渲染图形以及打印输出图纸，目前 已广泛应用于机械、建筑、电子、航天、造船、石油化工、土木工程、冶金、 地质、气象、纺织、轻工、商业等领域。 AutoCAD 2007是AutoCAD系列软件的最新版本，与AutoCAD先前的版本相比， 它在性能和功能方面都有较大的增强，同时保证与低版本完全兼容