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.
The results of standard experiments demonstrating relationships between dynamic (torque, moment of inertia) and kinematic (angular acceleration) characteristics of rotational motion can provide information on viscous friction acting on the rotating system. The standard experiments presented in this paper were performed using a symmetrical horizontal rotator with changeable moment of inertia (a bar with a symmetrically positioned pair of disc weights) supplied with optical gate; the rotator was driven by a permanent external torque in a resisting ambient atmosphere. The data were processed using the least squares method. The sums of squares of the residuals from the best-fit line (chiSquare values) were used to find out which experiments were influenced by laminar airflows and when turbulent airflows could occur along part of the rotating bar. The proposed experiment can be included in laboratory experiments in bachelor study programmes at colleges and technical universities.
The acoustic resonance in four glass Helmholtz resonators with diameters of 70, 52, 40, and 32 mm was detected in the frequency range of 360 to 1700 Hz using the simple experimental setup presented in this paper. The measured amplitudes of acoustic pressure required correction since the sound pressure amplitude of the loudspeaker used was not constant over the whole frequency range. The plots of the corrected acoustic pressure amplitude against frequency (resonance curves) showed expected amplitude enhancement (resonance) around the declared resonance frequencies of the resonators used. Fitting the theoretical dependence for the displacement amplitude of forced oscillations as a function of frequency to the plots of the corrected acoustic pressure amplitude against frequency provided the values of natural frequencies and damping constants of the resonators. The presented setup can be included in laboratory experiments or in a modified version as a demonstration experiment in physics lectures for undergraduate students.
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