In the previous lecture, we related the motion experienced by two observers in relative translational motion with respect to each other. In this lecture we will extend this relation to our third type of observer.That is, observers who accelerate and rotate with respect to each other. As a matter of illustration, let us consider a very simple situation, in which a particle at rest with respect

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

In addition to the equations of linear impulse and momentum considered in the previous lecture, there is a parallel set of equations that relate the angular impulse and momentum. Angular Momentum We consider a particle of mass, m, with velocity v, moving under the influence of a force F. The angular momentum about point O is defined as the \moment\ of the particle's linear

In this lecture we will consider the equations that result from integrating Newtons second law, F=ma, in time. This will lead to the principle of linear impulse and momentum. This principle is very useful when solving problems in which we are interested in determining the global effect of a force acting on a particle over a time interval Linear momentum We consider the curvilinear motion of a particle of mass, m, under the influence of a force F. Assuming that

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 lecture D2 we introduced the position velocity and acceleration vectors and referred them to a fixed cartesian coordinate system. While it is clear that the choice of coordinate system does not affect the final answer, we shall see that, in practical problems, the choice of a specific system may simplify the calculations considerably. In previous lectures, all the vectors at all points in the trajectory were expressed in the

Inertial reference frames In the previous lecture, we derived an expression that related the accelerations observed using two reference frames, A and B, which are in relative motion with respect to each other. aA =aB+(aA/ B)'y'' 22 x (DA/ B) 'y'2'+ TA/B+ X TA/B). (1) Here, aA is the acceleration of particle A observed by one observer, and

In this lecture, we will start from the general relative motion concepts introduced in lectures D11 and D12. and then apply them to describe the motion of 2D rigid bodies. We will think of a rigid body as a system of particles in which the distance between any two particles stays constant. The term 2-dimensional implies that particles move in parallel planes. This includes, for instance, a planar body moving within its plane

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

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