Statics And Rotations

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1 Statics And Rotations this lal ,.“/‘.‘.,. “,‘,,,‘.«““ o' ,’ ih ol ; aquilibirivum i ’ Glven Quantites ¢ Muss of Rectangular Metal Block O 4.1 Center Of Mass And Balance 9 < Figure 4.1: Balancing Stick For any particular object, its distribution of mass determines the position of its center of gravity, its angular momentum, and your ability to balance it. Place a lump of clay about the size of your fist around the meter stick, about 20 centimeters from the end. Balance the stick on the tip of your finger. First put your finger under the end near the clay. Now turn the stick over and balance it with the clay on the top. Notice that the stick is easier to balance when the clay is near the top. What?s Going On? The stick rotates more slowly when the mass is at the top, allowing you more time to adjust and maintain balance, When the mass is at the bottom, the stick has less rotational inertia and tips more quickly. The farther away the mass is located from the axis of rotation (such as in your hand), the greater the rotational inertia and the more slowly the stick turns. An object with a large mass is said to have a great deal of inertia. Just as it is hard to change the motion of an object that has a large inertia, it is hard to change the rotational motion of an object with a large rotational inertia. .

LA Moment Of necig And Paraiiel Axls Theciem | . 2 bl | [ IL.J IQ Figure 4.2; Meter stick with three holes You are provided a merer stick with 3 holes Hang one end of the stick from a stand by placing the horizontal bar through the hole, as shown in the left-most figure with a white cross, 1. Do NOT perform this task yet, but instead analyze it as a thought experiment. If all three forces (Fy, P, ) arc equal in magnitude, which of the three would cause the meter stick to rotate? Explain your reasoning | tINk ail of the forcer would cavse e e P(-mw LOCAMJIE WIETET AN $0r00 SHE aeae L o HE Where e MOL 1o 2 | o Yo @bpred 2. Which force will cause t le[wl('r stick to rotate the most? Why? I A i y YO4A4t v O ; r+4 The 5 $orte will cqype e metey : ‘((”"’\v%bvw,, fi\""v"w";fi’“f, Fo pn { g {141 ' 4 Now have each nu'm}wr in your group ‘take @ wirn app[w:g an e(/uuljum at (111 three locations of the meter stick and answer the last two questions again. 3. What is the fundamental definition of the moment of inertia? What two values or variables is it dependent on? What are its units? ; ; 10 i A ¢ N { ) Mo 21 of iner dys e / | (\VW ular accelevatioyr 't p leht ¥ oy )r»#\'li‘ ol arguliag feciry . uMiis= pgem= 4. What is the moment of inertia of the left-most meter stick shown in Fi igure 22 How did you figure this out? Represent this symbolically in terms of L and m. z 122 ’i/ mi

Lsif ¢ the parallel axds theorem, calculate the moment o ertla of the right 1 | Represent this symbolically in terms of L and m For any given shape, about what point is it easiest to rotate that hape about? Explain 1 taton veaau s { ’ av A ,;\“I' ( ! } A J / I U rer ! ¥l ¥ swer (0 the previous question; explain why the parallel 7. Based upon your al xis theorem ¢ the way it is Because We are $Yingto muuaty verpendicdlar mameni @ inertiad fov aréas 4.3 Static Equillibrium ?cm " Figure 4.3: Balancing Masses Take your meter stick and lay it flat against your table, with half on the table and half off of the table. Take the metal mass bar, mass = 500g, and place its center 10cm away from the center of the meter stick. Assume that the meter stick is massless 1. Before we get started, what is the equation for torque? What are the units of Torque? I SrEsing’ unts % 2. Using statics and torque, calculate the maximum weight that you can place 20cm to the right of the center of the meter stick to ensure that the system remains at rest Le. (in static equilibrium) (10) (4900) = ( 20)(X) X _‘LJSU/q S:E*lsf) 123

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B AL S50cm [ { Vi f A 10¢m I 7 om [ A Figure 4.4: Seesaw 4. You have been told in class that the point you select as the rotational point in your torque equation is rbitrary 1 5ees. sh Let's analyze this idea. For our purposes, assume that our meter stick can be modeled as above. Draw a Free Body Diagram for the system, write down and calculate the summation of the torques about each of the following points separately: Point A, Point B, and Point C. Explain why your answer should be the same about all of these points. (ty all 1he m € point A <10 (4q00) 5N =0 \ » ' poit B (Q) ’( : . v Nortroa Poiyr (= (rsw100) 0 "o Jmg 4.4 Moments Of Inertia And Rotational Motion ¢ We will now be analyzing the accelerations and motions of four equally sized discs rolling down an inclined ramp. The four discs are made of metal and plastic, and have the masses as shown above. Before we conduct any of these “races’, we will make predictions first. 1. If Metal Disc 1 and Metal Disc 2 were placed at the top of the incline and released simultaneously, which disc would reach the bottom first? Why? | Hﬂ,lﬂk Disc 2 would reach Hhe botH4om ISt cca £ there | ¢ ma iy e Hrom ¢ MirH f CorHo A o Hhe floor So 1t wunid decrra POYHIIN + 1 en ~ If Plastic Disc 1 and Plastic Disc 2 were placed at the top of the incline and released simultaneously, which disc would reach the bottom first? Why? \ PNk pladt \ 2 woutd redc e o A ecauie Smalley angultar Nentidvm malier o N 1 A A oet 3. If Metal Disc 1 and Plastic Disc 1 were placed at the top of the incline and released simultaneously, which disc would reach the bottom first? Why? e M€+l wou ch e ca v 4 i ) vy 124 e ¥

( ) [ ( \ 7 \ \ / Metal Disc 1 Metal Disc 2 Plastic Disc 1 Plastic [ Mass = 360 g Mass = 360 g Mass =120 g Mul AT r=2.5mm r=25mm r=2.5mm FRa 5 mm f-1.8 mm 7l L.1.8 mm Figure 4.5: Various hoops and disks 4. Il all four discs were placed at the top of an inclined ramp, and released simultancously which disc would reach the bottom first? Why? | € Y S piaste olisc 2 eca + hAas +he st paye the mallést ornguar moimept 1 ther mo ey o4 (n€ rua maljie y Now go 1o the ramp located in the classroom and test the four situations described above. 5. Did your predictions match what you observed? Why or why not? meAal Id ¢ yrimder went faster than i the prasugdise L 0 HeING A « e conol Nobecause tre . the ol w 6. Draw a Free Body Diagram of any of the above discs on an inclined ramp. Using the shapes’ specific moments ofinertia, and an arbitrary angle 0, calculate the linear and angular acceleration of the disk. Represent your answer in terms of mass m, 0 and radius r Fa a”'l”’)’filz 7. Let’ say the radius of Plastic Disc 1 were doubled, and you were to place the newly sized Plastic Disc 1 at the top alongside Metal Disc 1. If you released them simultaneously, which disc would reach the bottom of the ramp first? Why? fon i orasc pve 1 would reach Ahe bot: Jid haye gredt€r malg ana ya divg i vy 4.5 Spinning In A Chair We will now do a bir of experimenting with spinning in a chair. You can do this with orwithout weights. Throughout 1his lab you have hopefilly learned a great deal abou! statics, torque, moment of inertia, and rotational motion. Have vour group sit in a chair and spread their arms far away from their body. Have them slowly each teaym member g rotate themselves with rheir own foor (or your ream can gently rotate them). Once they are comfortable with a slow paced rotation and the ream nembers have all let go, have them pull their arms and legs as close to their body as possible 125

Ot @t Figure 4.6: Spinning in a chair 1. Explain what happens to the speed of rotation when your team member pulls their arms closer (g () Use the knowledge you gained throughout this lab to explain what happens (o their moment of gy angular momentum ,‘HJ,J (/1'f(!v,yh(”“‘ wzfij'”,‘f' rm e : e mass decveasirig rod s v vody Lecaure anquidr morm eptun? and tnevefore decreasg » 2. Name some rxmnp[u»,n[nhrn:lhlsprmci;rh‘ieuw([ in real life. WX €l This principle \s uied i) 1Le skannoy o danclr en Vbcle s ! ¥ e ) ale ] n avrm N o suddent ljmm rpe e 126

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