PHYSICS LAB Experiment 10 Fall 2004 ROTATIONAL DYNAMICS VARIABLE I, FIXED

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1 ROTATIONAL DYNAMICS VARIABLE I, FIXED In this experiment we will test Newtn s Secnd Law r rtatinal mtin and examine hw the mment inertia depends n the prperties a rtating bject. THE THEORY There is a crrespndence between variables in linear mtin and thse in rtatinal mtin: variable psitin velcity acceleratin Frce/ trque resistance t mtin kinetic energy Newtn nd s Law linear x v a F m ½ mv F=ma rtatinal I ½ I =I Trque is deined by The mment inertia is deined by Newtn s Secnd Law r several bdies rtating abut a cmmn axis, can be written: where is the net trque, is the angular acceleratin I is the ttal mment inertia abut the axis rtatin tt APPARATUS The apparatus cnsists a hrizntal bar attached t a rtatable drum radius r. Tw brass masses, M, are each placed a distance R rm th axis rtatin, and a mass, m, suspended rm a string wund arund the drum, causes the apparatus t rtate. A timer is used t measure the time, t, r the mass, m, t all a distance S, r equivalently, r the apparatus t rtate thrugh an angle. The pulley system increases the available distance, S. 1

2 DATA COLLECTION In this experiment, we keep the trque,, cnstant and vary I by changing the separatin, R, between the brass masses, M, in rder t veriy the R dependence the mment inertia, I. Use m = 0.050kg t apply a cnstant trque, = Tr = mgr. 1. Measure the mass the drum M drum and its radius r (t the pint attachment the string), the length L and mass M bar, and the sum the brass masses, M.. Set the brass masses at their minimum separatin and measure R (measure t the center the brass masses. Nte the distance between the hles in the bar). 3. With the drum initially at rest, measure the time r the drum t turn thrugh 5 cmplete revlutins, N. Repeat r a ttal 5 time measurements. 4. Use the average elapsed time t calculate the angular acceleratin (in units radian/sec ) as thrugh which the drum turns in N revlutins., where = N is the angle, in radians, 5. Repeat steps thrugh 4 r 4 larger values R, as well as with the brass masses remved, but with the same value m. The mment inertia can be expressed as the sum tw parts, I = I + M R, (1) where I is the mment inertia the drum and bar withut the masses, M, and each M cntributes MR t the mment inertia. The sum drum and bar mments inertia is where L is the length the bar. We can rewrite Newtn s Secnd Law ( =I ) as. (3) I the ttal trque is cnstant, and R is varied, we expect that the graph / as a unctin R shuld yield a straight line with slpe M, and intercept I. The net trque is given by = Tr where is the unknwn rictinal trque. Hwever, is expected t be small and we will assume =0, i.e. = Tr. Plt / as a unctin R, determine M rm the slpe, and cmpare with the actual value the mass. Determine I rm the intercept the graph. Calculate the mment inertia the hrizntal aluminum bar, and cmpare with the value I btained rm the ()

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4 PHYSICS LAB Expt 10 Wrksheet Fall 004 ROTATIONAL DYNAMICS VARIABLE I, FIXED STUDENT NAME DATE PARTNER S NAME LAB SECT Mass the drum, M drum = gm Radius the drum, r = (units ) Mass the bar, M bar = gm Length the bar, L = (units ) Sum the masses the brass cylinders, M = (units ) Trque, = (units ) Table 1: R R R Times / 1

5 PHYSICS LAB Expt 10 Wrksheet Fall 004 QUESTIONS 1. Cmpute the slpe the graph / as a unctin R and determine M rm the slpe.. Cmpare the value M determined in 1. with the measured value. Express the dierence as a percent dierence. D the values agree within 15 0%? 3. Determine I rm the intercept the graph. 4. Calculate the value I rm equatin (). Des the value agree with the value in 3.? Express the dierence as a percent dierence. 5. We used the value T = mg r the string tensin. In reality, the equatin mtin the mass m is given by where a is the linear acceleratin m and a = r. S, we have.t see hw much this aects the data, r yur largest value a, calculate the value a/(g a) At the end the lab, turn in yur wrksheet with the data and answered questins as well as yur graph.