Working on a vacuum manifold: See LLP chapter 9.2 for an excellent discussion on working with air-sensitive reagents, including how to use a two-way manifold. De-gassing solvents: The best way to remove water and oxygen from a solvent is to distill it over an appropriate drying agent (such as sodium). This can sometimes be a lengthy (and dangerous)task. Since we

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

Public Finance Defined Public finance is about the taxing and spending activities of the government. Also known as \public sector economics\or \public economics.\ Focus is on microeconomic functions of government- polices that affect overall unemployment or price levels are left for macroeconomics

1, Public finance,also known as public sector economics or public economics, focuses on the taxing and spending activities of government and their influence on the allocation of resources and distribution of income. 财政学,即公共经济学,焦点是税收和政府支出以及它们在分配资源和分配收入上的影响

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 will revisit the application of Newton's second law to a system of particles and derive some useful relationships expressing the conservation of angular momentum. Center of Mass Consider a system made up of n particles. A typical particle, i, has mass mi, and, at the instant considered, occupies the position Ti relative to a frame xyz. We can then define the center of mass, G, as the point

Non-Inertial Reference Frame Gravitational attraction The Law of Universal Attraction was already introduced in lecture D1. The law postulates that the force of attraction between any two particles, of masses M and m, respectively, has a magnitude, F, given by F= (1) where r is the distance between the two particles, and G is the universal constant of gravitation. The value of G is empirically determined to be

In the previous lectures we have described particle motion as it would be seen by an observer standing still at a fixed origin. This type of motion is called absolute motion. In many situations of practical interest, we find ourselves forced to describe the motion of bodies while we are simultaneously moving with respect to a more basic reference. There are many examples were such situations occur. The absolute motion of a passenger inside an aircraft is best

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

In this course we will study Classical Mechanics. Particle motion in Classical Mechanics is governed by Newton's laws and is sometimes referred to as Newtonian Mechanics. These laws are empirical in that they combine observations from nature and some intuitive concepts. Newton's laws of motion are not self evident. For instance, in Aristotelian mechanics before Newton, force was thought to be required in order