Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.