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Lecture# Acceleration in Cylindrical and Spherical Coordinates

Description

This lecture covers the concept of acceleration projected on the reference in cylindrical and spherical coordinates, including speed and acceleration components in both coordinate systems. The instructor explains the calculations and formulas involved in determining acceleration in different coordinate systems.

Official source

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In MOOCs (9)

Related concepts (21)

Instructor

Newton's Mechanics

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Point System Mechanics

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Rigid Body Mechanics

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Lagrangian MechanicsCe cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Newton's Mechanics

Ces quelques leçons de mécanique de Newton font partie d'un cours de formation de base en mécanique Newtonienne présenté sous la forme de 5 MOOCs:

- Mécanique de Newton
- Mécanique du point matérie

Del in cylindrical and spherical coordinates

This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by : it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by : it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.

Map projection

In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent.

Mercator projection

The Mercator projection (mərˈkeɪtər) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.

Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.

Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.

Related lectures (10)

Physics 1: Harmonic Oscillator and Spherical CoordinatesPHYS-101(g): General physics : mechanics

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Coordinate Systems: Cylindrical, Spherical, RotationsPHYS-101(f): General physics : mechanics

Covers cylindrical and spherical coordinates, position, velocity, and acceleration vectors.

Polar Coordinates: Position and VelocityPHYS-101(a): General physics : mechanics

Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.

Coordinate Systems and RotationsPHYS-101(f): General physics : mechanics

Covers cylindrical and spherical coordinates, vector positions, velocities, accelerations, and rotations.

Coordinate Systems: Polar, Cylindrical, SphericalPHYS-101(a): General physics : mechanics

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.