Precise measurement of velocity dependent friction in rotational motion

Abstract

Frictional losses are experimentally determined for a uniform circular disc exhibiting rotational motion. The clockwise and anticlockwise rotations of the disc, that result when a hanger tied to a thread is released from a certain height, give rise to vertical oscillations of the hanger as the thread winds and unwinds over a pulley attached to the disc. It is thus observed how the maximum height is achieved by the hanger decrements in every bounce. From the decrements, the rotational frictional losses are measured. The precision is enhanced by correlating vertical motion with the angular motion. This method leads to a substantial improvement in precision. Furthermore, the frictional torque is shown to be proportional to the angular speed. The experiment has been successfully employed in the undergraduate lab setting.

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].…”

Rotational dynamics with Tracker

“…A computerized technique that requires specific software is also used to determine the moment of inertia [8]. An interesting work, recently proposed by Alam et al [9], is the modification of the rotational dynamics apparatus made by Pasco to study the linear coefficient of rotational friction by letting the disc rotate freely after initial impulse excitation and then recording the reducing angular speed. Such an experiment could be called a 'let it roll' experiment.…”

Frictional torque on a rotating disc

“…where a and b are constants. Setting the right-hand sides of equations(2) and (6) equal to each other givesω(t ) = (ω 0 + a/b) exp(−bt/I) − a/b(7)after separating variables and integrating. The blue curve in figure 3 is a plot of this equation with the fitted values ω 0 = 34.94 ± 0.06 rad s −1 , a/I = 0.088 04 ± 0.000 15 s −2 , and b/I = 0.009 565 ± 0.000 010 s −1 .…”

“…A 'let it roll' experiment was used to quantify the frictional torque τ f by measuring the decrease in the angular speed ω of the disc as a function of time t after giving it an initial spin ω 0 . Based on a previous paper [2], it was assumed that the resistive torque varies linearly with the speed,…”