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Lecture# Motion Analysis: Cartesian and Polar Coordinates

Description

This lecture covers the analysis of motion using Cartesian and polar coordinates, focusing on kinematics, derivatives of vectors, trajectory, velocity vectors, acceleration vectors, and the concept of instantaneous velocity. It also explores the challenges of expressing acceleration components in polar coordinates for circular motion.

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In course

PHYS-101(e): General physics : mechanics

Le cours "Physique générale" fournit les notions de base nécessaires à la compréhension de phénomènes physiques comme la mécanique du point matériel. L'objectif est atteint lorsque que l'on peut prédi

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Related concepts (40)

Coordinate system

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring.

Acceleration

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by . A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".

Four-vector

In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined.

Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.

Related lectures (120)

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

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

Coordinate Systems: Polar and SphericalPHYS-101(e): General physics : mechanics

Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.

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.

Kinematics: Position, Velocity, AccelerationPHYS-101(j): General physics : mechanics

Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.

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

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