'Rotational Dynamics\r'

'revolutional Dynamics scheme Rotational kinetics is the study of the many a(prenominal) angulate equivalents that exist for transmitter dynamics, and how they relate to one an different. Rotational dynamics lets us view and consider a completely new set of physical applications including those that ask rotational accomplishment. The purpose of this audition is to investigate the rotational concepts of vector dynamics, and study the relationship among the ii quantities by using an Atwood machine, that contains two assorted heap attached. We employ the height (0. Mom) of the Atwood machine, and the medium fourth dimension (2. 5 s) the heavier eight took to seduce the bottom, to calculate the quickening (0. 36 m/SAA) of the Atwood machine. Once the acceleration was obtained, we use it to view the angulate acceleration or alpha (2. 12 radio detection and ranging/SAA) and implication of vehemence(torque) of the Atwood machine, in which past we were flattually su fficient to calculate the bet onment of inactiveness for the Atwood machine. In comparing rotational dynamics and analog dynamics to vector dynamics, it varied in the fact that additive dynamics happens only in one direction, objet dart rotational dynamics happens in many antithetical directions, bandage they ar some(prenominal) examples of vector dynamics.Laboratory Partners prophesy Kraal James Mulligan Robert Goalless Victoria Parr presentation The audition deals with the Rotational Dynamics of an intent or the visor gesture (rotation) of an object around its axis. vector dynamics, includes both Rotational and Linear dynamics, which studies how the ramps and torques of an object, affect the execution of it. Dynamics is related to Newtons act truth of motion, which states that the acceleration of an object produced by a net make is directly proportional to the magnitude of the net tweet, in the same direction as the net eviscerate, and inversely proportiona l to the dope of the object.This is where the famous equity of F=ma, force equals mass convictions acceleration, which directly deals with Newtons second law of motion. The important part of Newtons second law and how it relates to rotational dynamics and poster motion, is that Newtons second law of rotation is applied directly towards the Atwood machine, which is plainly a different form of Newtons second law. This equation for circular motion is: torque=FRR=l(alpha), which is important for helping us visualise what forces are playacting upon the Atwood machine. It is important to rise the formulas be take a shit it either refutes or upholdsNewtons second law of rotation and more(prenominal) than importantly helps us disc all over the moment of inertia and what it really means. Although both rotational and linear dynamics fall below the category of vector dynamics, thither is a big difference between the two quantities. Linear dynamics pertains to an object abject in a straight line and contains quantities such as force, mass, displacement, velocity, acceleration and momentum. Rotational dynamics deals with objects that are rotating or moving in a sheer path and involves the quantities such as torque, moment of inertia, angular velocity, angular acceleration, and angular momentum.In this lab we give be incorporating both of these ideas, but mainly focusing on the rotational dynamics in the Atwood Machine. E real range that we discover in the experiment is important for conclusion the moment of inertia for the Atwood machine, which describes the mass property of an object that describes the torque needed for a specific angular acceleration active an axis of rotation. This value impart be discovered by dismountting the two lot utilise on the Atwood machine and calculate the metric system of freights unitiness, then acquiring the average clock time it takes for the small weight to hit the ground, the height of theAtwood machine, the universal gas constant, the circumference, and the mass of the wheel. From these determine, you laughingstock calculate the velocity, acceleration, angular acceleration, angular velocity, and torque. Lastly, the law of preservation of energy equation is employ to find the formulas used to finally obtain the moment of inertia. Once these determine are obtained, it is important to under stick out the rotational dynamics and how it relates to vector dynamics. It is not only important to understand how and why they relate to distributively other, but to prove or disprove Newtons second law of motion and understand what it means.Purpose The purpose of this experiment is to study the rotational concepts of vector dynamics, and to understand the relationship between them. We will assume the relationships between the two quantities hold to be true, by using an Atwood machine with two different masses attached to discover the moment of inertia for the circular motion. Equipment The eq uipment used in this experiment is as follows: 1 Atwood machine 1 0. 20 kilogram weight 1 0. 25 kilogram weight 1 scale 1 piece of wander 1 stop watch with 0. 01 accuracy Procedure 1 . Gather all of the equipment for the experiment. 2.Mea original the weight of the two masses by using the scale, reservation sure to stripe as truely as possible. 3. Measure the continuance of the radius of the wheel on the Atwood machine. Then by and by obtaining this number, double it to obtain the circumference. 4. After cadence what is need, die to set up the Atwood machine properly. Ask the TA for assistance if needed. 5. First start by secure the end of the string to both weights, double knotting to bring out sure that it is tight. 6. Set the string with the weights attached to the crease of the Atwood machine wheel, making sure that it is properly in place. 7.Then set the lighter mass on the allot end of the machine, and hold in place, so that the kickoff point is at O degrees. 8. Make sure that the stopwatch is take a shit to start recording time. 9. When both the timer and the weight dropper are ready to start, release the weight and start the time in sync with one another. 10. At the exact time the mass makes connexion with the floor, stop the time as accurately and precise as possible. 1 1 . Repeat this process three times, so that an average can be obtained of the three run times, making the data a much more accurate representation of the time it takes he weight to hit the ground. 2. Now that the radius, masses, and time are recorded, it is time to actualize the calculations of the data. 13. Calculate the velocity, acceleration, angular acceleration, moment of force or torque, and finally moment of inertia. 14. Finally, compare the relationships of the rotational concepts inquired and sweep conclusions. Notes and Observations The Atwood machine contained four outer cylinders that stuck out of the wheel, which cause air resistance in rotation, and co ntribute to the moment of inertia. The timer, was hard to stop at the exact remediate time when the weight made contact with he floor.Lastly, thither was friction of the string on the wheel, when the weight was released and it rubbed on the wheel. Data Mass of the first weight: 250 g=O. Keg Mass of the second weight: egg=O. Keg Weight 1=MGM= 2. 45 N Weight 2=MGM= 1. 96 N Time 1: 2. 20 seconds Time 2: 2. 19 seconds Time 3: 2. 06 seconds Height: 82. 4 CM= 0. 824 m Radius: 17 CM= 0. 17 m Circumference (distance)= 0. 34 m Mass of the wheel= 221. G x 4= egg= 0. Keg 2 x (change in a= (change in 0. 36 urn,92 a=r x (alpha) alpha= alarm = 2. 12 radar/92 Velocity=d/t -?0. 58 m/s E(final) E(final) + Work of friction (l)g(change in height)= h + m(2)g(change in height) + h + h law v/r Moment of Inertia= 0. 026 keg x m/SAA summation of . 876 Error Analysis on that point was erroneousness to forecast for in this lab, which first started with the four cylinders that stuck out of the Atwood machi ne in a circular pattern. This caused air resistance in which we could not account for. We only measured the weight of the four cylinders for the impart weight of the Atwood machine, because the wheel itself was massages in comparison.Even though it accounted for very little error in our experiment, it effected the other number that we calculated in our data, making them a little less accurate. When finding the amount of time it took the heavier weight to make contact with the rubber pad, there was human error in the reaction time of the timer in which we accounted for, making our data more accurate and precise. This is why we averaged all of the values in order to make the times more precise. Lastly, there was error for the friction of the string making contact with the wheel, which we did not account for, because there was no carriage of accounting for it.The reason why the force f the tension and the weight were not equal to each other was because of this friction force that e xisted, which we were not able to find. Conclusion Throughout this experiment we examined the circular dynamics of a pendulum when outside act upon it, making the pendulum come upon in a circular motion. We measured many values, including the period, in order to determine the theoretical and observational forces acting on the pendulum. From this we were able to draw conclusions about how the data-based and theoretical forces relate to each other.We as well were able to test Newtons second law of motion determining whether or not t holds to be true. The values that we obtained to get our experimental and theoretical forces started with linguistic context up the cross bar set-up, and attaching the string with the pendulum to the force gauge and obtaining the tension in the string which was 3 Newtons, by reading the off of the gauge, while the pendulum was char in a circle. We then measured the mass of the pendulum with a balance scale to be 0. 267 kilograms, which were then able to find the weight to be 2. 63 Newtons.Next we were able to find the length of the string and force gauge attached to the pendulum. Instead of measuring conscionable the string attached to the pendulum, we also measured the force gauge, because without it our readings would be inaccurate. After placing the wall grid under the pendulum, we received the numeric value of 0. 5 meters of the radius by reading it off of the chart, by measuring from the origin, to the end of the where the pendulum hovered the graph. Then we found the period by using the stopwatch, which was 1. 71 seconds. We started the time at the line of the first crossbar and ended it at the same place.With these numbers that we measured we were able o calculate the lean of the string to the crossbars when it was in motion to be 35. 5 degrees. Then we found the constant velocity by using V = nor/t, in which we obtained the value of 1. 84 meters/second. From this we used the formula a = Ã¢â‚¬ËœГ˜2/r to calc ulate the constant acceleration which was 6. 67 m/SAA, which we came to the understanding that the pendulum was moving very quickly, and that it took a while to slow down. From this we used Newtons famous second law, which was F=ma, to solve for the Force that was subjected on the pendulum.We knew that if this value was flippantly close to our experimental value that his theory would be proven correct. Me modified the equation to fit for the detail that was involved, in which we used F = m x Ã¢â‚¬ËœГ˜2/r to receive the value of 1. 81 Newtons. Lastly, by using all of the data that we obtained from the experiment, we used the formula Force Experimental= Ft(sin B) to get an experimental force value of 1. 74 Newtons, which lead us to believe we solved for the correct formulas, and followed the procedure for the experiment correctly. Some of the discrepancy in our data comes from the mental unsoundness of the crossbar set- up.This is because our crossbar holders were not in place correctly, which we couldnt correct, so we obtained our data as accurately as we could. Another error in our data came from the force gauge, in that it didnt stand still when we set the pendulum in motion. We couldnt read barely what was on the force gauge and it also unplowed changing numbers, so we had to estimate based on what we saw. Lastly, the error in reaction time of the stopwatch changed our data. Without these errors existing, I believe our experimental values would be closer to our theoretical values. Even though this whitethorn be true, our values were only different by 0. Newtons, meaning we performed the experiment correctly for the most part. From the results that we obtained from the experiment, we immediately understand what we would have to do to improve our results in collecting data and obtaining the Experimental Force acting on the pendulum. Our error could have been improved by using a different table with more stability, improving our reaction time, an d obtaining multiple values for the force gauge then averaging the results. We figured out that even though there was error in our experimentation, that our values were still pretty accurate Judging by the theoretical value.Theoretical values are based on what is discovered by physicists performing the experiment over and over again. So to use these values and get a number only fractions off, shows that the way we performed our experiment was not very far off. We proved Newtons second law to be true, because by doing the experiment and getting similar values shows that his concept holds to be true. The forces that we used to move the pendulum showed the dynamics of the pendulum, and how this can be used to understand concepts of the planets rotating around the sun in the universe, Just at a much smaller scale.\r\n'