Author: Physics Notebook

The motion of the particle is described by the three equations,  , and So the displacement of the particle can be written as, where, , and are the unit vectors in three dimensional Cartesian co-ordinate system along the X-axis, Y-axis and Z-axis respectively. Again the velocity is the time derivative of the displacement vector, so…

The motion of the particle is described by the three equations,  , and So the displacement of the particle can be written as, where, , and are the unit vectors in three dimensional Cartesian co-ordinate system along the X-axis, Y-axis and Z-axis respectively. Again the velocity is the time derivative of the displacement vector, so…

Here the position vector of the point is given by,   So the velocity is  Now, at t=3sec. So the magnitude of the velocity is, Again we know that acceleration is the time derivative of the velocity vector. So the acceleration is given by, So at t=3 sec. the acceleration is So the magnitude of…

The velocity of the moving particle is given by, Since the velocity is the time derivative of the position vector  , then we can write, where, is a constant.

We know that if a particle moves along a curve in a plane, then the expression for the velocity of the particle is given by, [ To know the derivation for the velocity (CLICK HERE) ] and the expression for the acceleration is given by, [ To know the derivation for the acceleration (CLICK HERE)…

Let us consider a point is moving in a plane, If (x,y) be the cartesian co-ordinates of the point and be the plane polar co-ordinates in the two-dimensional system, then the relation between the speeds in cartesian and polar co-ordinates is given by, the radial component of speed along is and the transverse component of…

Let us consider a point P having the two-dimensional cartesian co-ordinates (x,y). The polar co-ordinates of that point in the two dimensional system are . here, and . Differentiating equations (1) & (2) with respect to time we get, and, Multiplying equations (3) and (4) by and respectively and then adding them we get, […

Let us consider the Cartesian co-ordinates of the point are , Given, the spherical polar co-ordinates of that point are We know that, So the Cartesian co-ordinates of the point are [ To know the relation between the three-dimensional cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]

Let us consider the Cartesian co-ordinates of the point are , Given, the spherical polar co-ordinates of that point are We know that, And, So the cartesian co-ordinates of the point are [ To know the relation between three-dimensional cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]

The movement of a particle in a polar co-ordinate system is described by, and We know that the radial component of velocity is and the transverse component of velocity is . And the radial component of the velocity is and the transverse component of the acceleration is Now, Again, Now, Again, So the radial component…