We have performed molecular dynamics simulations of atomistic models of $C_{60}$ molecules and DMPC bilayer membranes to study the static and dynamic effects of carbon nanoparticles on biological membranes. All four $C_{60}$-membrane systems were investigated representing dilute and concentrated solutions of $C_{60}$ residing either inside or outside the membrane. The concentrated $C_{60}$ molecules in water phase start forming an aggregated cluster. Due to its heavy mass, the cluster tends to adhere on the surface of the bilayer membrane, hindering both translational and rotational diffusion of individual $C_{60}$. On the other hand, once $C_{60}$ molecules accumulate inside the membrane, they are well dispersed in the central region of the bilayer membrane. Because of the homogeneous dispersion of $C_{60}$ inside the membrane, each leaflet is pushed away from the center, making the bilayer membrane thicker. This thickening of the membrane provides more room for both translational and rotational motions of $C_{60}$ inside the membrane compared to that in the water region. As a result, the dynamics of $C_{60}$ inside the membrane becomes faster with increasing its concentration.