Motion of solid object in fluid is studied in moving frame of reference. Navier-Stokes (N-S) equations in a non-inertial frame of reference is coupled with the equations of linear and angular momentums for the solid object. It is shown that the numerical implementation for solving the non-inertial N-S equations is equivalent to that of the arbitrary Lagrangian-Eulerian (ALE) method. The simulation results by the two methods show reasonable agreements for a 2-D flow field including a cylinder. In the present work, a generalised convective boundary condition is constructed for non-inertial frame of reference. Also, an appropriate boundary condition is proposed for fluid phase based on a least square adjustment (LSA) method. It is shown that the LSA is essential for the non-inertial study fluid-solid interaction. Also, the non-inertial N-S equation is applied to a problem of a concave object falling in a fluid. It is shown that traditional time-advancement schemes undermine the ortho-normality of the rotation matrix, resulting in non-physical deformation of the object. However, our time-advancement procedure with quaternion is found to be robust and effective even under a violent manoeuvre of the object.