Certain neutron stars (extremely dense stars)I are believed to be rotating at about 0.83 rev/s. Ifsuch a star has a radius of 39 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation? Number n? I Units kg V eTextbook and Media Assistance Used Hint Assistance Used Consider a particle of mass m on the equator of the star. It moves in uniform circular motion, with a centripetal acceleration, because of the gravitational force on it from the rest of the star. Do you see how the acceleration is related to the force by Newton's second law? Key Ideas . The gravitational acceleration a, of a particle (of mass m) is due solely to the gravitational force acting on it. When the particle is at distance r from the center of a uniform, spherical body of mass M, the magnitude F of the gravitational force on the particle is given by Eq. 13.1.1. Thus, by Newton's second law, F = mag, which gives GM ag . Because Earth's mass is not distributed uniformly, because the planet is not perfectly spherical, and because it rotates, the actual free-fall acceleration g of a particle near Earth differs slightly from the gravitational acceleration d g , and the particle's weight (equal to mg) differs from the magnitude of the gravitational force on it