PRINCIPLES OF MOMENT

International Letters of Chemistry Physics and Astronomy, 2013

This work has been performed to verify the existent knowledge on determination of the mass moment. For the experiment, a compound pendulum was used. The motivation to undertake these studies were experimental results indicating a big discrepancy in mass moments between the values coming from calculations using the definition formula and these obtained from the experiment. In relation to the axial moment the relative error equals 23.6 %, whereas regarding the polar moment the error reached 56.4 %. Considering the reason of that discrepancy we could find the existent theory not to be adequate. The theory is then considered in view of verifying first the mathematical pendulum and next the physical/ compound pendulum theory. The consideration has been focused on the description of accelerated motion cycle of both pendulums as it was enough to solve the problem. A source differential equation, which serves to solve any quantum phenomena, was used in the study. Then the course of creation of detailed characteristics of the phase of mathematical pendulum accelerated motion is presented as the basis to derive formula on the mass moment of a compound pendulum. At the end this new adequate theory was verified showing the relative error to be less than one per cent.

The physical model for the subdivision of the kilogram into the decade from 1 kg to 100 g was adapted for the measurement system where weight support plates have to be used. That is the case when combinations of weights with different nominal masses are compared. For this purpose the calibration procedure was modified to eliminate the unknown masses of the support plates. The equation was derived to take into account various influences on the measured mass differences. The influence of the plates on the measurement uncertainty budget and on the estimates of unknown masses of weights was studied into the decade. The analysis of results shows that the application of the support plates influences the measurement uncertainty to a small extent and also confirms the adequacy of the used model.

Worksheet Worked examples Practical: Using the principle of moments to determine the mass of a clamp stand End-of-chapter test Marking scheme: Worksheet Marking scheme: End-of-chapter test Chapter 5 Forces, moments and pressure

Review of Scientific Instruments, 2007

An analytical expression relating mass and position of a particle attached on a cantilever to the resulting change in cantilever resonant frequency is derived. Theoretically, the position and mass of the attached particle can be deduced by combining measured resonant frequencies of several bending modes. This finding is verified experimentally using a microscale cantilever with and without an attached gold bead. The resonant frequencies of several bending modes are measured as a function of the bead position. The bead mass and position calculated from the measured resonant frequencies are in good agreement with the expected mass and the position measured.

2008 Annual Conference & Exposition Proceedings

He holds a B.S. degree in Mechanical Engineering from Oklahoma Christian University and M.S. and Ph.D. degrees in Mechanical Engineering from The University of Michigan, Ann Arbor. His interests include stress analysis, nonlinear dynamics, structural vibration, and engineering design.

Applied Physics Letters - APPL PHYS LETT, 2010

Resonant microcantilevers are highly sensitive to added masses and have the potential to be used as mass-spectrometers. However, making the detection of individual added masses quantitative requires the position determination for each added mass. We derive expressions relating the position and mass of several added particles to the resonant frequencies of a cantilever, and an identification procedure valid for particles with different masses is proposed. The identification procedure is tested by calculating positions and mass of multiple microparticles with similar mass positioned on individual microcantilevers. Excellent agreement is observed between calculated and measured positions and calculated and theoretical masses.

IOP Conference Series: Materials Science and Engineering

The application of an atomic force microscope (AFM) based microcantilever system for the determination of mass of gold nanoparticles (AuNPs) has been demonstrated. In this system, standard AFM microcantilevers for measurements in vacuum have been employed. The limit of mass determination with our AFM-based system has been determined to be of the order of 10-10 g. The prospects of employing AFM cantilever-based sensors for highly sensitive protein detection in proteomic studies and in diagnostics have been discussed.

Exhibition Catalog: Measuring and Weighing in Ancient Times, Reuben and Edith Hecht Museum, University of Haifa, 2001

Jurnal Neutrino

A study of mass measurement using strain gauge 120 which was placed in the corner of the brass cantilever has been done. This study essentially utilizes deflection phenomena on the surface. This phenomenon occurs due to the mass placed on one end of the brass cantilever. The Mass was calibrated with standard mass gauge using OHAUS PA214 Pioneer<sup>TM</sup> analytical balance. It was done a variation of mass-reduction and addition at the end of the brass cantilever with a multiple of 0.1 gram over a span interval of 1.1-7.5 grams. It obtained hysteresis curve plot for the changing strain gauge resistance (ΔR) versus mass variations on which the system has the maximum load range (7,1-7,5 gram). Moreover, The test of the system for the mass variations in the output voltage of the IC AD521JD differential amplifier was approximated as a quadratic function which was expressed in the system characteristic equation m = 2,4×V<sup>2</sup> - 0,8533×V + 1,1449, with m ...