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In this research, the rotation of a solid particle in a vortex flow is investigated computationally. The bvp4c MATLAB scheme is employed for mathematical modeling and physical analysis. After solving the governing equations, the influences of some physical parameters like initial values of radius, radial velocity and angular velocity as well as the ratio of drag force to inertia force on the velocity and displacement characteristics of the particle will be analyzed. The findings indicate that increasing $r_0$ and ${\omega }_0$ causes an increase in radial velocity, but increasing $u_0$ and ${\alpha }^2$ have conversed treatments. Also, the angular velocity enhances by increasing the ratio of drag-to-inertia forces.