Rigid body dynamics r and velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the reference point R are and If R is chosen as the center of mass these equations simplify to To specialize these formulas to a rigid body, assume the particles are rigidly connected to each other so P, i=1...,n are located by the coordinates r and velocities v. Select a reference point R and compute the relative position and velocity vectors, where ω is the angular velocity of the system. The linear momentum and
Escape velocity alternative expression for the escape velocity formula_6 particularly useful at the surface on the body is: where "r" is the distance between the center of the body and the point at which escape velocity is being calculated and "g" is the gravitational acceleration at that distance (i.e., the surface gravity). For a body with a spherically-symmetric distribution of mass, the escape velocity formula_6 from the surface is proportional to the radius assuming constant density, and proportional to the square root of the average density ρ. where formula_14 The escape velocity "relative to the surface" of a rotating body depends on