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What Is Rectangular Cartesian Co-Ordinates System?
Rectangular cartesian co-ordinate system: In classical mechanics, it is considered that there are three dimensions in space. These three dimensions are represented by three axes in the cartesian co-ordinate system. These three axes are X-axis, Y-axis and Z-axis, which are mutually perpendicular to each other. The origin is denoted by the fixed point where these…
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What Is The Plane Polar Co-Ordinate System?
Plane polar co-ordinate system: In the study of two-dimensional cases, we observe the motion takes place in a plane. Sometimes the plane polar co-ordinate is very suitable for this purpose. In this plane polar co-ordinate system, the two co-ordinates for a point are: (i) r is the radial distance of the point A from the…
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What Is Spherical Polar Co-Ordinate System? What Are Their Limits?
Spherical polar co-ordinate: The spherical polar co-ordinate system is a method of representation, which helps to represent the co-ordinates of a point on the surface of a sphere. There are three co-ordinates in this system. The three co-ordinates for a point A in the spherical polar co-ordinate system are given bellow: The radial distance of…
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Derive The Relation Between Three Dimensional Cartesian Co-ordinates And The Spherical Polar Co-ordinates.
Relation between polar co-ordinates and three-dimensional Cartesian co-ordinates: Let us consider, x, y, and z to be the Cartesian co-ordinates of the point A as shown in the adjoining figure. OB is the projection of OA in the X-Y plane, since OA makes an angle with the positive Z-axis, so . Since is the azimuthal…
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Find The Value Of Position Vector In Two-Dimensional And Three-Dimensional Cartesian Co-Ordinate System.
Position vector in two-dimensional cartesian co-ordinate system: A particle is moving in a plane so we will use a two-dimensional co-ordinate system in this case to describe the motion of the particle. Let us consider the motion in X-Y plane. Let at any instant of time and be the Cartesian co-ordinates of the particle P.…
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Define Unit Vectors In Planer Motion In Terms Of Their Cartesian Counter-Parts.
In a two-dimensional plane polar co-ordinate system, there are two unit vectors The radial unit vector . The direction of this unit vector is along the radius vector The unit vector along the direction of increasing . Similarly, in case of planer motion in a two-dimensional Cartesian co-ordinate system, there are also two…
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What Are The Unit Vectors In Spherical Polar Co-ordinates? Express These Unit Vectors In terms Of Unit Vectors In Three-Dimensional Cartesian Co-Ordinate System.
Unit Vectors In Spherical Polar Co-Ordinate System: In spherical polar co-ordinate system, there are three unit vectors, Radial unit vector along the direction of radius vector . along the direction increasing . along the direction of increasing . The unit vector is perpendicular to unit vector . The unit vector is perpendicular to the both…
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Show That The Spherical Polar Unit Vectors Are Mutually Perpendicular To Each Other.
Unit vectors in spherical polar co-ordinate system are mutually perpendicular to each other: Two unit vectors are said to be orthogonal to each other when the angles between these two unit vectors are , i.e., they are perpendicular to each other. In order to prove the unit vectors (, , ) in spherical polar co-ordinate…
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Show That Plane Polar Unit Vectors Are Orthogonal.
The unit vectors in plane polar co-ordinate system are orthogonal: In a plane polar co-ordinate system, the radial unit vector is and the angular unit vector is [ To know the derivations of the above unit vectors CLICK HERE ] Where, and are the unit vectors along the X-axis and Y-axis in two-dimensional cartesian co-ordinate…
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Derive The Expression For The Displacement Of A Particle Moving Along A Curve In A Plane.
Displacement Of a particle moving along a curve in a plane: Let us consider a point A in a two-dimensional Cartesian co-ordinate system, the position of this point can be described by a specific single vector. This vector is the displacement of that point A with respect to the origin O of the co-ordinate system,…
