Statics And Rotations

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Apr 3, 2024

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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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