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Motion in three dimensions



8. Motion in three dimensions

  • We have already studied physical quantities like displacement ,velocity,acceleration etc in one and two dimension
  • In this topic ,we will generalize our previous knowledge of motion in 1 and 2 -dimension to three dimension's
  • As we have used vectors to represent motion in a plane,we can freely use vectors and its properties in 3-dimension as we have done in case of motion in a plane
  • In three dimensions ,we have three units vectors i ,j and k associated with each co-ordinate axis of Cartesian co-ordinates system shown below in the figure


    Motion in three dimensions

  • Consider a particle moving in 3-D space .Let P be its position at any point t.Position vector of this particle at point P would be
    r=xi+yj+zk
    Where x,y and z are co-ordinates of point P
  • Similarly velocity and acceleration vectors of particle moving in 3-D space are
    v=vxi+vyj+vzk where vx=dx/dt,vy=dy/dt and vz=dz/dt
    and
    a=vxi+ayj+azk
    where ax=dvx/dt,ay=dvy/dt and az=dvz/dt
  • All the relations we have derived in case of motion in plane are valid for 3-D motion with one added co-ordinate





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