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Uncertainty principle (summary)
Posted on Friday April 10, 2015

Heisenberg Uncertainty Principle or indeterminacy principle was given by German scientist Warner...

Lorentz Transformation
Posted on Thursday April 09, 2015

Derivation of Lorentz transformation equations using orthogonal transformations Let us consider...

NET/JRF Physics : Relativistic Lagrangian and equation of motion
Posted on Tuesday April 07, 2015

This article is about the solution of the problem where you have to find the equation of motion...


Motion in a plane


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1. Introduction

  • In previous chapter we have learned about the motion of any particle along a straight line
  • Straight line motion or rectilinear motion is motion in one dimension.Now in this chapter ,we will consider both motion in two dimension and three dimension.
  • In two dimensional motion path of the particle is constrained to lie in a fixed plane.Example of such motion motion are projectile shot from a gun ,motion of moon around the earth,circular motion and many more.
  • To solve problems of motion in a plane,we need to generalize kinematic language of previous chapter to a more general using vector notations in two and three dimensions.


2.Average velocity

  • Consider a particle moving along a curved path in x-y plane shown below in the figue
  • Suppose at any time,particle is at the point P and after some time 't' is at point Q where points P and Q represents the position of particle at two different points.




  • Position of particle at point P is described by the Position vector r from origin O to P given by
    r=xi+yj
    where x and y are components of r along x and y axis
  • As particle moves from P to Q,its displacement would be would be Δr which is equal to the difference in position vectors r and r'.Thus
    Δr = r'-r = (x'i+y'j)-(xi+yj) = (x'-x)i+(y'-y)j = Δxi+Δyj                                          (1)
    where Δx=(x'-x) and Δy=(y'-y)
  • If Δt is the time interval during which the particle moves from point P to Q along the curved path then average velocity(vavg) of particle is the ratio of displacement and corresponding time interval


    since vavgr/Δt , the direction of average velocity is same as that of Δr
  • Magnitude of Δr is always the straight line distance from P to Q regardless of any shape of actual path taken by the particle.
  • Hence average velocity of particle from point P to Q in time interval Δt would be same for any path taken by the particle.


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