218100 - Frederiksen

Teacher NotesScience conceptsCenter of mass - assumed known.Moment of inertia, Steiner’s theorem and period forphysical pendulum - formulae are summarized.Reversion pendulum - the formula for the oscillationperiod is derived.Mathematical prerequisitesEquation Solving, trigonometric functions, use ofspreadsheets, graphs.Derivation of the formulae for moments of inertia requiresintegral calculus.Didactic considerationsCalculation of the moment of inertia of the rod canbe simplified by ignoring the holes. This causes anerror in the rod moment of inertia about the centre ofjust over 1%.Calculated oscillation periods of the rod alone willincrease by up to 0.5%. (The greatest deviation forpivot in the centre hole.) With weights mounted onthe rod, period deviations will be less.An even more obvious simplification can be done byconsidering bolts, nuts and washers as point masses.The error in calculations of moment of inertia willbe less than 0.08%, the period error is half of that.These errors will probably be negligible comparedto measurement uncertainties and other sources oferror when working with the general physical pendulum.Note that these errors are irrelevant when the deviceis used as a reversion pendulum !!!It seems tempting to expand the calculations of experiment2 – Symmetrical mass distribution by findingthe moment of inertia of the weight about itsown centre. This requires subtraction of two nearlyequal values, and will therefore be subject to veryhigh uncertainty. It is only recommended if you wantto dig into uncertainty calculations – otherwise, thediscrepancy between theory and measurement willonly create frustration.The best procedure is to repeat experiment 2 for allthe possible values of x L, then I Gcan be plotted asa function of x L2. The interception with the y-axis isthen I R+ 2 I W.On www.frederiksen.eu you will find a completespreadsheet for calculating moments of inertia etc...Search for part number 2181.00LiteratureD. Candela, K. M. Martini, R. V. Krotkov, and K. H.Langley:Bessel’s improved Kater pendulum in the teachinglabAmerican Journal of Physics - June 2001 - Volume69, Issue 6, pp. 714Equipment listThe following is suggested:2181.00 Physical pendulum / Bessel pendulum0015.10 Clamp2002.50 Electronic Counter1975.50 Fotocell unit0016.00 Table clamp0023.10 Universal bosshead (2 are used)0008.50 Retort Stand Rod 25 cm0008.20 Retort Stand Rod 75 cmA/S Søren Frederiksen, Ølgod Tel. +45 7524 4966 info@frederiksen.euViaduktvej 35 · DK-6870 Ølgod Fax +45 7524 6282 www.frederiksen.eu®