The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. Suppose a scientist makes a slight error in sample preparation and one sample has a mass \(10\,\text{mg}\) larger than the opposing sample.

If the samples are \(12\,\text{cm}\) from the axis of the rotor and the ultracentrifuge spins at \(60000\,\text{rpm}\), what is the magnitude of the net force on the rotor due to the unbalanced samples?