Frictional torque on a rotating disc

Abstract

Resistance to motion often includes a dry frictional term independent of the speed of an object and a fluid drag term varying linearly with speed in the viscous limit. (At higher speeds, quadratic drag can also occur.) Here, measurements are performed for an aluminium disc mounted on bearings that is given an initial twist and allowed to spin until it comes to a stop. It is found that a sum of both the dry and fluid resistive terms are needed to accurately fit the entire data. However, the speed-independent term alone suffices over any suitably limited range of motion, permitting one to use the standard kinematic equations for constant angular acceleration. The measurements and theory are appropriate for an introductory physics laboratory at the college level.

Unfurling a rolled-up sheet from a dispenser at constant speed

“…Equation ( 19) is an illustration of the powerful simplification that can arise by normalizing variables in physics. If preferred, equation (19) can be rewritten as a function of elapsed time t using equation (16) or of the total angle θ of rotation of the roll using equation (7).…”

“…The solution presented in this article could be modified to treat materials which resist unrolling such as adhesive tape, kitchen plastic wrap, inflexible metal foil, a stiff tape measure, or a rolled-up magnetic strip. The analysis could also be generalized to account for kinetic friction between the inner tube and the rod or bracket on which it is mounted [7], or for rolling friction in bearings [8] used to couple the roll to the axle. The problem shares some features with those involving yo-yos [9], spools pulled by their threads so that they roll without slipping along a table [10,11], carpet rolls given a push so that they unfurl along a floor [12,13], harpoon guns [14], or yarn being pulled off the spindle of a spinning wheel.…”

“…thickness h of the paper, one can count the number of initial wraps on the roll, with equation(7). Substituting equations(15) and (17) into (12) results in the dimensionless relation…”

Conservation laws and energy transformations in a class of common physics problems

“…While the above derivation above may be considered a relatively simply model for inelastic collisions compared to more realistic models, it still required solving differential equations well beyond the scope of most introductory physics classes. By contrast, for the rotational system, we consider a simplified dry friction model 15 that generates a constant torque on the system and brings the disks to common angular velocity linearly in time. This case of constant torque can be analyzed using algebra as a case of rotational kinematics.…”

Optimization of a Magnetodynamic Receiver for Versatile Low-Frequency Wireless Power Transfer

“…The loss parameters are identified experimentally by impulse response method the ball-bearing-guided rotor [12]. The magnet-mounted rotor, initially launched in rotation at 100 Hz, induces a voltage in a nearby pick-up coil.…”