Curvilinear motion in polar coordinates pdf

The rod can slide back and forth to illustrate the planar and. For motion in a circular path, r is constant the components of velocity and acceleration become. Note that the radial direction, r, extends outward from the fixed origin, o, and the transverse coordinate, q,is measured counterclockwise ccw from the horizontal. Jan 20, 2015 to analyze curvilinear motion using normal and tangential coordinate system. Wellknown examples of curvilinear coordinate systems in threedimensional euclidean space r 3 are cylindrical and spherical polar coordinates. The n and t coordinates move along the path with the particle tangential coordinate is parallel to the velocity the positive direction for the normal coordinate is toward the center of curvature me 231. Thats where im drawing a blank and why i thought the given r equation had to be manipulated in some way to be in terms of t. Note that the radial direction, r, extends outward from the fixed origin, o, and the transverse coordinate. Todays learning outcomes are to describe the kinematic relationship of acceleration in a tangential and normal coordinate system. Being able to change all variables and expression involved in a given problem, when a di erent coordinate system is chosen, is one of.

I also know that the dot means the derivative is taken in respect to time. Cartesian coordinates we will start by studying the motion of a particle. The polar coordinate system is defined by the coordinates r and just like the nt coordinate axes, the r and. If all motion components are directly expressible in terms of horizontal and vertical coordinates 1 also, dydx tan. The taxis is tangent to the path curve at the instant considered, positive in the direction of the particles motion. Curvilinear motion in polar coordinates it is sometimes convenient to express the planar twodimensional motion of a particle in terms of polar coordinates r. Hi, this is module five of two dimensional dynamics. We can express the location of p in polar coordinates as r r u r. The directions tand nlie in the local plane of the curve. Me 230 kinematics and dynamics university of washington. Usage will depend on the situation usually, more than one can be used. The third description of plane curvilinear motion is the polar coordinates. Sometimes, more than one is needed at the same time.

We shall see that these systems are particularly useful for certain classes of problems. Chungnam national university velocity rr r rr vr u u uu curvilinear motion. Description of particle motion often is simpler in noncartesian coordinate systems, for example, polar coordinates. Note that the radial direction, r, extends outward from the fixed origin, o, and the transverse coordinate, q, is measured counterclockwise ccw from the horizontal. To analyze curvilinear motion using normal and tangential coordinate system. It is an absolute prerequisite to kinetics, which is the study of the relationships between the motion and the corresponding forces that cause the motion or are. A slotted link on a fixed pivot causing a rod to slide along the curve is an example of curvilinear motion. 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. 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.

Curvilinear motion describes the motion of a moving particle that conforms to a known or fixed curve. For example in lecture 15 we met spherical polar and cylindrical polar coordinates. A typical nt problem will either give the exact location of the particle on a path, or it will give kinematics information from which the position can be determined. A polar coordinate system is a 2d representation of the cylindrical coordinate system. Top 15 items every engineering student should have. We think of a particle as a body which has mass, but has negligible dimensions. Feb 27, 2018 top 15 items every engineering student should have. When the path of motion is known, normal n and tangential t coordinates are often used in the nt coordinate system, the origin is located on the particle the origin moves with the particle the taxis is tangent to the path curve at the instant considered, positive in the. Lecture l5 other coordinate systems in this lecture, we will look at some other common systems of coordinates. Normaltangential nt coordinates are attached to, and move with, a particle. Curvilinear coordinates fujiun jiang october 11, 2010 i. Treating bodies as particles is, of course, an idealization which involves an approximation.

Dynamics path variables along the tangent t and normal n. Where the particle is located by the radial distance r from a fixed point and by an angle measured from the radial line. Therefore there is no position vector in nt coordinates. When the particle moves in a plane 2d, and the radial distance, r, is not constant, the polar coordinate system can be used to express the path of motion of the particle. Same as that obtained with n and tcomponents, where the. Curvilinear motion acceleration components youtube. Another reason to learn curvilinear coordinates even if you never explicitly apply the knowledge to any practical problems is that you will develop a far deeper understanding of cartesian tensor analysis. Note that the radial direction, r, extends outward from the fixed. Most particles experience curvilinear motion in three dimensions. For instance, the point 0,1 in cartesian coordinates would be labeled as 1, p2 in polar coordinates. Gradient, divergence and curl in curvilinear coordinates. It is a simple matter of trigonometry to show that we can transform x,y. We will present polar coordinates in two dimensions and cylindrical and spherical coordinates in three dimensions.