Eksperiment ROT: Rotation Kinematics. Experiment ROT: Rotation Kinematics

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1 Experiment ROT: Rotation Kinematics Introduction: In this experiment you will investigate the rotation of a disc slowed down by friction. Eksperiment ROT: Rotation Kinematics Inleiding: In hierdie eksperiment word die rotasie van ʼn skyf wat deur wrywing afgerem word, ondersoek. Experimental Aims: The aim of this experiment is to: 1. Measure the angular speed of a disk by measuring the time taken for a sector to pass through a photo gate. 2. Determine the angular acceleration of the disk by measuring the angular speed as a function of time. Skills Developed: 1. Using computer-based measuring equipment to determine the speed of a rotating disk. 2. Data processing, drawing graphs and determining the slope of a graph. 3. Interpretation of data. 4. Drawing conclusions from results. Theoretical background: You need to read up on the theory behind the practical beforehand. All the required information is in Halliday Resnick & Walker (use the index to find it). Your knowledge on the topics will be tested in the prepractical test. You should be able to do the following: Explain what angular displacement is, and in what units it is measured. Explain what angular velocity is and state the units in which it is measured. Write down a formula for angular velocity of a disk if the angular displacement in a certain time interval is known. Explain what quantity each of the symbols represent and state the SI units in which they are measured. Write down a formula for angular acceleration if the angular velocity as a function of time is known. Explain what quantity each of the symbols represent and state the SI units in which they are measured. Eksperimentele Doel: Die doel van hierdie eksperiment is om: 1. Die hoeksnelheid van ʼn skyf te meet deur met ʼn fotohek die tyd te meet wat dit neem vir ʼn sektor van die skyf om by ʼn punt verby te beweeg. 2. Die hoekversnelling van die skyf te bepaal uit hoeksnelheidsmetings wat op verskillende tye geneem is. Vaardighede Ontwikkel: 5. Gebruik van rekenaargebaseerde instrumentasie om die spoed van ʼn roterende skyf te bepaal. 6. Dataverwerking, teken van grafieke en bepaling van die helling van ʼn grafiek. 7. Interpretasie van data. 8. Maak van gevolgtrekkings van resultate. Teoretiese agtergrond: U moet oor die teoretiese agtergrond agter die eksperiment oplees. Al die nodige inligting is in Halliday, Resnick & Walker (gebruik die indeks om dit te vind). U kennis oor die werk sal deur middel van ʼn vooraf-toets bepaal word. U moet in staat wees om die volgende te doen: Verduidelik wat hoekverplasing is, en wat die eenhede daarvan is. Verduidelik wat hoeksnelheid is en noem die eenhede waarin dit gemeet word. Skryf ʼn formule neer vir die hoeksnelheid van ʼn skryf as sy hoekverplasing in ʼn gegewe tydinterval bekend is. Verduidelik watter hoeveelheid elkeen van die simbole voorstel en noem die SI-eenhede van elk. Skryf ʼn formule neer vir die hoekversnelling van ʼn skryf as die hoeksnelheid van die skyf as ʼn funksie van tyd bekend is. Verduidelik watter hoeveelheid elkeen van die simbole voorstel en noem die SI-eenhede van elk. Apparatus A round, transparent Perspex disc that has alternate opaque and transparent sectors. A photo gate connected to a computer to take time measurements. Apparaat ʼn Ronde deurskynende Perspex-skyf met afwisselende deurskynende en ondeurskynende sektore. ʼn Fotohek wat aan n rekenaar gekoppel word om tydmetings te doen.

2 Van: Surname: Voorletters: Initials: PHY 114 Praktikum / Practical ROT Datum: 2014 Date Handtekening van student: Signature of student: Van van TA: Surname of TA: Studentenommer: Student Number: Rotasie / Rotation [I].*ROTI*..* *. mm dd Praktikumsessie: Practical session: Groepnommer: Group number: TA Paraaf: TA Initial: MEMO Praktikum: Practical: Vooraftoets (/10): Pre-test (/10): Praktikum (/40): Praktical (/40): ROT Apparatus A round, transparent Perspex disc that has alternate opaque and transparent sectors. A photo gate connected to a computer to take time measurements. Apparaat ʼn Ronde deurskynende Perspex-skyf met afwisselende deurskynende en ondeurskynende sektore. ʼn Fotohek wat aan n rekenaar gekoppel word om tydmetings te doen. Part A: Experimental Setting up the system: 1. The photo gate is already connected to the computer via the interface box. (If not, please ask your assistant for help). 2. Switch on the computer and run the Science Workshop program (icon on desktop). 3. In the Science Workshop program, go to the File menu, select Open and open the newrot.sws file. 4. Check that the Setup window of the program (the one with the Record and Stop buttons) is active. If not click in it with the mouse to activate it. 5. Spin the disk. 6. Click on the REC button to start the recording and the STOP button to stop the recording. (Record about 7 seconds of the disk spinning.) 7. The computer will record the time interval between successive interruptions of the beam (i.e. the time required for a transparent and an opaque sector to pass). 8. Click on the Graph window to show a graph of your readings. 9. Click on the Table window to show the results in table form. Change the number of significant figures to show at least three digits after the decimal. Experiment: The computer measures the time interval between successive beam interruptions. We want to plot a graph of angular velocity (in radians per second) as a function of time. Rotate the disk so that a transparent sector is beneath the photo gate. Use a piece of paper to interrupt the beam for one second, then remove the paper again for a second repeating four of five times. Use the computer to record the results. Deel A: Eksperiment Opstelling: 1. Die fotohek is reeds deur middel van die koppelvlak aan die rekenaar verbind. (Indien nie, vra asseblief u assistent vir hulp.) 2. Skakel die rekenaar aan en voer die program Science Workshop uit (ikoon op die desktop). 3. In die Science Workshop program, gaan na die File-menu, kies Open en maak die newrot.sws-lêer oop. 4. Maak seker dat die Setup-venster van die program aktief is. (Dit is die een met die REC en STOP-knoppies.) Indien nie, kliek op die venster om dit te aktiveer. 5. Laat die skyf vry draai. 6. Kliek op die REC -knoppie om die opname te begin en op die STOP -knoppie om die opname te staak. (Neem omtrent 7 sekondes op terwyl die skyf vry draai.) 7. Die rekenaar sal die interval tussen opeenvolgende onderbrekings van die straal bepaal. (D.w.s. die tyd wat dit neem vir ʼn deurskynende en ʼn ondeurskynende sektor om deur die fotohek te beweeg, word bepaal.) 8. Kliek op die Graph-venster om ʼn grafiek van u lesings te sien. 9. Kliek op die Table-venster om u resultate in tabelvorm te sien. Verander die aantal tellende syfers om ten minste drie syfers na die desimaal te wys. Experiment: Die rekenaar meet die tydinterval tussen opeenvolgende onderbrekings van die straal. Ons wil ʼn grafiek stip van hoeksnelheid (in radiale per sekond) as ʼn funksie van tyd. Draai die skyf só dat ʼn deurskynende sektor in die fotohek is. Gebruik ʼn stuk papier om die straal vir een sekonde lank te onderbreek, en dan weer vir ʼn sekonde lank deur te laat en dan weer te onderbreek ens. Herhaal vir vier tot vyf onderbrekings. Gebruik die rekenaar om die data van die fotohek op te neem.

3 [A1] Explain the readings that you got and how they correspond with the beam interruptions you produced. Does the computer measure the time interval between successive interruptions correctly? Readings are approx.. 2s, i.e. correspond to the time from one interruption to the next. [A1] Verklaar die lesings wat u verkry en hoe hulle met die onderbrekings van die straal ooreenstem. Het die rekenaar die tydinterval tussen opeenvolgende onderbrekings van die straal korrek gemeet? [A2] Consider the rotating disk. What change in angular position will correspond to the time interval measured by the computer? Give your answer in degrees as well as in radians. 2*Pi x 1/(number of black sectors) = [A2] Beskou die roterende skyf. Met hoeveel verander die hoek-posisie van die skyf in die tydinterval wat deur die rekenaar gemeet word? Gee u antwoord in grade sowel as in radiale. 360 x 1/(number of black sectors) = [A3] How is the angular velocity of the disk calculated from the measured data? [A3] Hoe word die hoeksnelheid van die skyf van die gemete data bereken? θ Change in angle ω= = t Time interval [A4] How is angular acceleration calculated from the angular velocity? [A4] Hoe word hoekversnelling van die hoeksnelheid bereken? α ω ω2 -ω1 = = t t [A5] We want to draw a graph of angular velocity as a function of time. Use the computer to collect about 7 s of data while the disk is spinning freely at around 1 2 revolutions per second. (You may check the linearity of your data using the Graph window on Scientific Workshop.) Collect the necessary data in a neat table and do the calculations to calculate the average angular velocity and average angular acceleration as a function of time in SI units (use radians for angular measurements). Take about 10 readings. (Space for table on next page) [A6] Which variable (angular velocity or time) is the independent variable and which one is the dependent variable? (The dependent variable is the one whose value changes when you vary the independent variable.) [A5] Ons wil ʼn grafiek teken van hoeksnelheid as ʼn funksie van die tyd. Gebruik die rekenaar om omtrent 7 s lank data op te neem terwyl die skyf vry roteer teen ʼn spoed van 1 2 omwentelinge per sekonde. (U kan die lineariteit van u data nagaan deur die na die Graph-venster van Scientific Workshop te gaan.) Versamel die data in ʼn netjiese tabel en maak die berekeninge om die gemiddelde hoeksnelheid en die gemiddelde versnelling as ʼn funksie van tyd in SI eenhede te bepaal. (Gebruik radiaal vir hoekmetings.) Neem omtrent 10 lesings. (Plek vir tabel op volgende bladsy.) [A6] Watter veranderlike (hoeksnelheid of tyd) is die onafhanklike veranderlike en watter een is die afhanklike veranderlike? (Die afhanklike veranderlike is die een wat verander as mens die onafhanklike veranderlike variëer.) Time independent Angular velocity - dependent

4 Table 1: Tabel 2: Interval # Time, t (s) Time interval, t, (s) Avg. Angular velocity, ω (rad/s) Avg. Angular acceleration, α (rad/s 2 0 [A7] Draw a graph representing the relationship between the angular velocity of the disk and the time. (Ensure that the independent variable is on the horizontal axis!). (Graph paper on next page.) [A8] What shape does your graph have? [A7] Stip ʼn grafiek wat die verband tussen die hoeksnelheid van die skyf en die tyd te toon. (Verseker dat die onafhanklike veranderlike op die horisontale as gestip word.) (Grafiekpapier op volgende bladsy.) [A8] Wat is die vorm van u grafiek? Approx. linear [1] [A9] Does your graph go through the origin? (Explain why it should or should not.) No. At time t=0 the disk is not standing still, so ω 0 [A9] Gaan u grafiek deur die oorsprong? (Verduidelik hoekom dit die geval moet wees / nie wees nie.) [A10] What relationship between angular velocity and time does the shape of your graph suggest? [A10] Wat is die verband tussen die hoeksnelheid en die tyd volgens u grafiek? Linear, ω= ω0 αt, where α is a constant

5 Graph of ω as a function of t. [5] [A11] Draw a best fit line through your experimental data points and find its slope. Don t forget the units! Explain the sign of the slope. Graph of ω as a function of t. [A11] Teken ʼn passingslyn deur u eksperimentele datapunte en vind die helling van die lyn. Moenie die eenhede vergeet nie! Verduidelik die teken van die helling. [A12] From your answer in the previous question, write down the empirical (observed) relationship between angular velocity and the time. (We call this equation an abstract model.) ω= ω0 αt, where α is a constant Negative angular acceleration, i.e. rotation slows down. [A12] Gebruik u antwoord in die vorige vraag om die empiriese (waargenome) verband tussen hoeksnelheid en die tyd neer te skryf. (Ons noem hierdie vergelyking die abstrakte model.)

6 [A13] Draw a graph representing the relationship between the angular acceleration of the disk and the time. (Ensure that the independent variable is on the horizontal axis!). [A13] Teken ʼn grafiek wat die verband tussen die hoekversnelling van die skyf en die tyd voorstel. (Verseker dat die onafhanklike veranderlike op die horisontale as gestip word.) Graph of \alpha as a function of time. Alpha should not change much [5] [A14] What do you conclude from the shape of your graph? Is the acceleration related to the slope of the angular velocity vs time graph? Explain. [A14] Wat kan u van die vorm van die grafiek aflei? Is daar ʼn verband tussen die hoekversnelling en die helling van die hoeksnelheid teen tyd grafiek? Verduidelik. Angular acceleration is negative and roughly constant (maybe decreasing in magnitude slightly over time )

7 [A15] Summarise your conclusions in 2 3 sentences. [A15] Som u gevolgtrekkings in 2 3 sinne op. E.g. Angular velocity of disk was found to decrease linearly => approx. constant (negative) angular acceleration Close the Science Workshop programme without saving changes. Maak die Science Workshop program toe sonder om enige veranderinge te stoor. Total marks:40