Why does a smaller centrifuge rotor tolerate a higher rotational speed than a larger rotor?

The primary limitation to the rotational speed of a centrifuge rotor is the structural strength of the material from which it is constructed, as the rotor must withstand the stress of the centrifugal force generated during operation.1

In a rotor of a given design, the maximum angular velocity that can be achieved before the material ruptures is approximately inversely proportional to the rotor's diameter. Because of this relationship, a smaller rotor can be safely operated at a higher angular velocity than a larger one. Specifically, a rotor with half the diameter of a larger one can be rotated at twice the angular velocity, which results in the production of twice the centrifugal force at the periphery.1