The paper develops dynamic and mathematical models of the physical inclined pendulum. The motion equations of a pendulum are solved by a stage-by-stage consideration method. The motion laws and amplitudes of oscillations, coordinates of the stagnation zone and their graphical representations are analyzed and discussed. The expressions of oscillation characteristic: period, amplitude, decrement of damping oscillations, quality of a pendulum are determined and considered depending on the angle of inclination and length of the thread, radius of the pendulum ball, rolling friction coefficient and other system parameters. For practical applications, working formulas have been found for determining the rolling friction coefficient at rest, the dynamic rolling friction coefficient and the rolling friction coefficient at the stagnation zone. As an example, the values of the coefficient of rolling friction of solid steel on steel are given. The investigation results can be used to develop new educational laboratory work, to design and create new instruments for determining rolling friction coefficients used in mechanical engineering.

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