Laboratory experiment for the study of friction forces using rotating apparatus

Abstract

The standard experimental set-up enabling observation of rotational motion of a bar around its centre of mass, which is set into motion due to the external torque generated by the small weight, was extended with an optical gate and position sensor and connected to a computer with software, which made it possible to display measured values of bar half-rotations during accelerated and decelerated motion as well as to process the data immediately. The detailed analysis of experimental data obtained for decelerated rotational motion due to frictional torque only (without small weight) showed that, besides the constant term due to dry friction at an axle, the expression for friction forces in the system has to include terms depending on the first and/or second power of angular speed, which is evidence that viscous forces influence the motion of a bar. The frictional torque due to viscous forces can be evaluated as the difference between the effective frictional torque acting on the system and the frictional torque due to dry friction at an axle. The data obtained in the experiment in which the bar performed damped oscillatory motion provided the values of effective frictional torque and the moment of inertia of rotating bodies. The frictional torque due to dry friction can be obtained as a minimum torque (calculated using minimum mass of weight) needed to start rotational motion. The last two proposed experiments can be included in undergraduate laboratory practicals.

Viscous friction in standard rotational motion experiments

“…The experiment presented in this paper was carried out using commercially available rotation apparatus (3B Scientific [4]). The obtained results, besides illustrating standard relationships between angular acceleration, torque and moment of inertia, reveal that friction forces, both dry (constant) as well as viscous (velocity-dependent, though small and usually neglected), do play a role in this kind of motion, as already reported in [5][6][7][8][9]. The proposed data processing using SciDAVis 1.D013 free software [10], which provided chiSquare values [11], enables us to find out which experiments are influenced by laminar airflows and when turbulent airflows occur [12] along part of the rotating bar depending on the Reynold's number value [13].…”

“…´-11.81 10 Nm, 4 which is larger than the value ´-4.19 10 Nm 4 of dry friction for this apparatus [6], is an indication that viscous friction torque, which averaged value is…”

“…• The contribution from viscous friction torque acting on the rotating part of the apparatus was obtained as the difference between the friction torque M f calculated using equation (7) and the dry friction torque f 0 (estimated from the minimum mass attached to the cord which is needed to start the rotational motion of the cross bar [6]). • The chiSquare (c 2 ) values were used to assess the fits of theoretical functions equation (18) which take into account not only dry but also laminar friction torques acting on the rotating system, to experimental data.…”

“…The standard experiments which can be performed using this apparatus enable students to determine the angular acceleration a as a function of torque τ, which sets the bar into motion, and to determine the moment of inertia I as a function of the distance R of the disc weights with mass m 2 d from the axis of rotation. The apparatus also makes it possible to perform measurements which provide information on the friction forces acting on the rotational motion of a rigid body [6].…”

“…The rotating apparatus can be considered as a system of bodies (figure 1) with the weight m descending with acceleration of magnitude a and the bar with discs rotating with angular acceleration a for which it holds a = a r where r is the spindle radius. The equations of motion of this system have the following form [6]:…”