This worksheet is intended as a brief introduction to dynamics in spherical coordinates.
Notice that r is a minimum when … Objectives • Concepts such as position, displacement, velocity and acceleration are introduced • Study the motion of particles along a straight line. ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington. Now, let's learn another coordinate that will describe the rotational motion, which is polar coordinate. But in polar coordinate you have an origin, and then from the origin you have …

A male gymnast completes a complicated move involving simultaneous rotation and translation.
Polar coordinate is a very, very popular to describe the rotational motion. Let (r,θ) denote the polar coordinates describing the position of a particle. In some problems with circular symmetry, it is easier to formulate Newton’s laws of motion in a coordinate system that has the same symmetry. Note that a fixed coordinate system is used, not a “body-centered” system as used in the n –t approach. List of Links. If the particle is constrained to move only in the r –q plane (i.e., the z coordinate is constant), then only the first two equations are used (as shown below). In lecture 4, we do a series of examples where velocity and acceleration using polar and cylindrical coordinates, then ending with an introduction to normal and tangential unit vectors. Be respectful to each other post strictly within Statics and Dynamics, a nonrelevant post will be deleted. Let r1 denote a unit vector in the direction of the position vector r , and let θ1 denote a unit vector perpendicular to r, and in the direction of increasing θ, see Fig. Mechanics 1: Polar Coordinates Polar Coordinates, and a Rotating Coordinate System. This is the community to discuss both parts of Engineering Mechanics: Statics and Dynamics. Courses » Engineering Dynamics Notes & Problems » Polar Coordinates Polar Coordinates . Graphical representation • Investigation of a particle … Here we derive equations for velocity and acceleration in polar coordinates and then we solve a few problems. 1. x y O θ i j r 1 θ 1 rcosθ r rsinθ Figure 1: First, we want to derive expressions … Questions about understanding the concept, theory, formulae derivation, and problem-solving. The coordinate system in such a case becomes a polar coordinate system. Lecture 3: Particle Kinematics • Kinematics of a particle (Chapter 12) - 12.7-12.8 W. Wang. So suppose that you have a point A has a velocity of v vector here, and then note that in t coordinate your et vector is this is defined along with the v vector. Video: An Intuitive Derivation of the … Polar coordinates are a complementary system to Cartesian coordinates, which are located by moving across an x-axis and up and down the y-axis in a rectangular fashion. This is a conic section of eccentricity e in polar coordinates (r,θ) (see page 668). e = C2 GM or r +recosθ = C2 GM or r = C2/(GM) 1+ecosθ. Definition and Sketch . Consider a point P on the surface of a sphere such that its spherical coordinates form a right handed triple in 3 dimensional space, as illustrated in the sketch below.