The position of a particle is given by the position vector r. We have provided all the pdf links to download study material for all the 1st year engineering b. Conceptual physics textbook chapter 2 second edition, laboratory book and conceptdevelopment practice book. The name curvilinear coordinates, coined by the french mathematician lame, derives from the fact that the coordinate surfaces of the curvilinear systems are curved. This approximation may be perfectly acceptable in some situations and not adequate in some other cases. The velocity, v, and the acceleration, a, for curvilinear motion are defined as. Curvilinear motion occurs when a particle moves along a curved path. We think of a particle as a body which has mass, but has negligible dimensions. To analyze curvilinear motion using normal and tangential coordinate system. Plane curvilinear motion coordinates used for describing curvilinear motion rectangular coords nt coords polar coords studying the motion of a particle along a curved path which lies in a single plane 2d. Me 230 kinematics and dynamics university of washington. This is a special case of the more general 3d motion.
Describe the motion of a particle traveling along a curved path. This means that one can convert a point given in a cartesian coordinate system to its. Displacements, velocity and acceleration, their relationship relative motion curvilinear motion newtons laws of motion work energy equation impulse and momentum impact of elastic bodies. We will start by studying the motion of a particle. The curved path can be in two dimensions in a plane, or in three dimensions. Jan 15, 2015 conceptual dynamics independent learning. A disk of radius 3 cm is glued to another disk of radius 6 cm, with a common axis, as shown in the figure. Jan 20, 2015 to analyze curvilinear motion using normal and tangential coordinate system. In this work, we present algorithms for locating and tracing particles through curvilinear and unstructured hexahedral meshes. In this section students will learn about particle kinematics, newtons laws and eulers laws, motion.
Two positions in the trajectory of a circular motion. Only one degree of freedom is needed in order to give the position in any instant. Curvilinear motion problem 4 kinematics of particles youtube. Curvilinear motion force and acceleration methods for particles 1 engineering mechanics. Applications the path of motion of a plane can be tracked with radar and its x, y, and z coordinates relative to a point on earth recorded as a function of time. Find materials for this course in the pages linked along the left. This means that when describing the motion of a particle using noncartesian coordinates, we must. The power screw starts from rest and is given a rotational speed which increases uniformly with time t according to, where k is a constant. In the next few paragraphs we will discuss the kinematics of a particle motion in all these di erent frames. In geometry, curvilinear coordinates are a coordinate system for euclidean space in which the coordinate lines may be curved.
Engineering mechanics pdf 1st year notes pdf download books. The most famous examples of planar motion are related to the motion of two spheres that are gravitationally attracted to one another, and the generalization of this problem to planetary motion. Plane curvilinear motion rectangular coordinates xy if all motion components are directly expressible in terms of horizontal and vertical coordinates time derivatives of the unit vectors are zero because their magnitude and direction remains constant. R r since we have a constant speed v 0, we have s v 0t. The freeflight motion of a projectile is often studied in terms of its rectangular. The hallmark of a relativistic solution, as compared with a classical one, is the bound on velocity for massive particles. Since the motion is often threedimensional, vectors are used to describe the motion. Rectlinear motion is motion that only moves in a straight line, its similar to curvilinear motion wich is motion that only moves in a curved line.
Only after the fbd has been completed should the equations of motion be written. Special cases of motion i there are some special cases of motion to consider 1 the particle moves along a straight line. By curvilinear motion we refer to the motion of an object along a curve. For instance, if we want to study the motion of planets, it is. Example circular motion we consider motion of a particle along a circle of radius r at a constant speed v 0. Displacement the displacement represented the change in the particle s positions. An airplane of weight w 200,000 lb makes a turn at constant altitude and at constant velocity v630 fts. Use of elevators in public places is an example of rectilinear motion. The particle motion is approximated in phase space, while the fluid flows or fields are calculated on a fixed eulerian frame of reference. Determine the expressions for the velocity v and acceleration a.
The particle is located by the radial distance r from a fixed point and by an angular measurement. Consider the motion along a curved path, sometimes called curvilinear motion, such as a motion along apb of figure 24. Mit opencourseware aeronautics and astronautics 16. When equations of motion are expressed in terms of any curvilinear coordinate system, extra terms appear that represent how the basis vectors change as the coordinates change.
To investigate particle motion along a curved path using different coordinate. What are the examples of rectilinear and curvilinear motion. Curvilinear kinematics investigates lows of motion of objects in space in two and three directions without any reference to forces that cause the motion to change. Threedimensional curvilinear motion describes the most general case of motion for a particle. Vector calculus examples xviii chapter 19 relative motion of a particle 191. The rst step in describing the motion of a particle is to identify its position at any time t. Video created by georgia institute of technology for the course engineering systems in motion. The particle may be a particle, a person, a car, or some other moving object.
Free body diagram unveils every force that acts on the isolated particle. An introduction to curvilinear orthogonal coordinates overview. For motion in a circular path, r is constant the components of velocity and acceleration become. Use coupon code newuser and access any one subject free for 3 days. Wellknown examples of curvilinear coordinate systems in threedimensional euclidean space r 3 are cylindrical and spherical polar coordinates. Engineering mechanics pdf material is available for all the students who are visited this page at free of cost. Curvilinear motion acceleration components youtube. Nov 29, 2018 a model for inertial particles in curvilinear flows. Consider the freeflight motion of a projectile which is initially launched with a velocity v0 v0 cos. Stop by the office recycling box on your way to class and pickup enough sheets of paper to give one to each member of the class and have some left over. To provide the problemsolving strategy when working with normal and tangential components.
This course is an introduction to the study of bodies in motion as applied to engineering systems and structures. Acceleration is always collinear with the velocity. See centrifugal force, twobody problem, orbit and keplers laws of planetary. We know that if the particle moves a distance dx along the x axis. Lecture notes dynamics mit opencourseware free online. Relate kinematic quantities in terms of the rectangular components of the vectors. The recent popularity of inertial microfluidic devices has driven attention towards the behavior of particles in flows within curvilinear microchannels for particle separation and concentration applications. Curvilinear motionis the motion where particles move along a curved path. This paper presents a direct numerical simulation dns for the chaotic viscoelastic flow. Freely browse and use ocw materials at your own pace. F mutual force of attraction between two particles g universal constant of gravitation experiments g 6. The horizontal bar a moves to the right at 10 ms, keeping in contact with the bigger disk and without sliding on its surface.
Influenced by the microstructures of viscoelastic fluid, the passive particles scalar transportation carried by the flow will be greatly enhanced. The free flight motion of projectile is studied in terms of its rectilinear components. The total time of the motion from a to f and the average velocity in that motion. These coordinates may be derived from a set of cartesian coordinates by using a transformation that is locally invertible a onetoone map at each point. Treating bodies as particles is, of course, an idealization which involves an approximation. The motion of the particle can also be described by measurement along the tangent tand normal nto the curve as shown in the gure below. Curvilinear motion and projectiles velocity acceleration. Here all units see here is original time on time interval. Gravitational forces acting on objects resulting in free fall is an example of rectilinear motion. Motion of connected particles examples xix chapter 20 curvilinear motion of a particle 201. Kids sliding down from a slide is a rectilinear motion. Pdf a model for inertial particles in curvilinear flows.
Dynamics of particles and bodies in 2d motion from georgia institute of technology. Rectilinear motion under constant and varying acceleration. Equations of motion in cartesian coordinates 2dof aircraft model 4. Motion of passive particles carried by viscoelastic fluid. Description of particle motion often is simpler in noncartesian coordinate systems, for example, polar coordinates. Curvilinear motion is defined as motion that occurs when a particle travels along a curved path. Kinematics displacement, velocity, acceleration, 1 and 2dimensional motion source. Relativistic solutions lecture 11 physics 411 classical mechanics ii september 21st, 2007 with our relativistic equations of motion, we can study the solutions for xt under a variety of di erent forces. The polar coordinate system is defined by the coordinates r and just like the nt coordinate axes, the r and. Threedimensional curvilinear motion describes the most general case of motion for a. P4 kinematics lecture notes 2 scope of the lecture course.
Coordinates used for describing curvilinear motion rectangular coords nt coords polar coords studying the motion of a particle along a curved path which lies in a single plane 2d. A particle moves along a curve defined by the path function, s. Problem 5 on curvilinear motion video lecture from chapter. The students completing this course are expected to understand the concepts of forces and its resolution in different planes, resultant of force system, forces acting on a body, their free body diagrams using graphical methods. The robust technique of inertial focusing is particularly advantageous in such applications, not only because curved geometries can greatly reduce the footprint of a. Curvilinear motion general curvilinear motion curvilinear motion is defined as motion that occurs when a particle travels along a curved path. The position of the particle at any instant is designated by the vector r rt. In the case of uniform motion in a straight line, the average speed is the same as the instantaneous speed. A model for inertial particles in curvilinear flows.
Both the magnitude and direction of r may vary with time. Such objects may be considered as particles, provided motion of the body is characterized by motion of its center of mass and any rotation of the body is neglected. Some examples of curvilinear motion are as follows. For instance, if we want to study the motion of planets.
1126 1116 1577 978 1072 609 360 1219 1044 1111 877 959 6 249 15 1487 168 1049 855 1548 654 1434 597 1024 688 115 1161 1245 554 710 1098 878 1396