Rotational Dynamics

Rotational Dynamics Abstract Rotational kinetics is the study of the many angular equivalents that live for transmitter dynamics, and how they relate to one an otherwise. Rotational dynamics lets us view and consider a entirely new treated of physical applications including those that involve rotational motion. The purpose of this investigate is to investigate the rotational concepts of s destructioner dynamics, and study the relationship between the 2 quantities by development an Atwood shape, that contains two divers(prenominal) stooles attached. We use the height (0. Mom) of the Atwood machine, and the average measure (2. 5 s) the heavier eight took to hit the bottom, to face the acceleration (0. 36 m/SAA) of the Atwood machine. Once the acceleration was obtained, we used it to find the angular acceleration or alpha (2. 12 radar/SAA) and moment of run( crookedness) of the Atwood machine, in which so we were eventually fitted to channelise the moment of inertia for the Atwood machine. In compare rotational dynamics and linear dynamics to vector dynamics, it varied in the fact that linear dynamics happens alone in one direction, magic spell rotational dynamics happens in many different directions, while they are two examples of vector dynamics.Laboratory Partners Divine Kraal James Mulligan Robert Goalless Victoria Parr Introduction The experiment deals with the Rotational Dynamics of an object lens or the billhook motion (rotation) of an object around its axis. Vector dynamics, includes some(prenominal) Rotational and Linear dynamics, which studies how the surprises and torques of an object, affect the motion of it. Dynamics is related to Newtons second law of motion, which states that the acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the alike direction as the net force, and inversely proportional to the mass of the object.This is where the famous law of F=ma, for ce equals mass times 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 circular motion, is that Newtons second law of rotation is applied directly towards the Atwood machine, which is Just a different form of Newtons second law. This equation for circular motion is torque=FRR=l(alpha), which is important for helping us extrapolate what forces are acting upon the Atwood machine. It is important to test the formulas because it either refutes or provesNewtons second law of rotation and more importantly helps us excise the moment of inertia and what it really means. Although both rotational and linear dynamics fall under the category of vector dynamics, there is a big difference between the two quantities. Linear dynamics pertains to an object moving in a straight line and contains quantities such as force, mass, displacement, velocity, acceleration and momentum. Rotational dyna mics deals with objects that are rotating or moving in a curved mode and involves the quantities such as torque, moment of inertia, angular velocity, angular acceleration, and angular momentum.In this lab we will be incorporating both of these ideas, but mainly focusing on the rotational dynamics in the Atwood Machine. Every value that we discoer in the experiment is important for finding 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 ab bulge an axis of rotation. This value will be discovered by getting the two masses used on the Atwood machine and calculating the clog, then getting the average time it takes for the smaller weight to hit the ground, the height of theAtwood machine, the rundle, the circumference, and the mass of the wheel. From these values, you can calculate the velocity, acceleration, angular acceleration, angular velocity, and torque. Lastly, the l aw of conservation of energy equation is used to find the formulas used to eventually obtain the moment of inertia. Once these values are obtained, it is important to consider the rotational dynamics and how it relates to vector dynamics. It is not only important to look how and why they relate to each 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 equipment 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 puff 1 stop watch with 0. 01 accuracy Procedure 1 . Gather all of the equipment for the experiment. 2.Measure the weight of the two masses by using the scale, making sure to measure as dead-on(prenominal)ly as possible. 3. Measure the length of the radius of the wheel on the Atwood machine. Then after obtaining this number, double it to obtain the circumference. 4. After measuring what is need, proceed to set up the Atwood machine properly. Ask the TA for assistance if needed. 5. First start by tying the quit of the range to both weights, double knotting to make sure that it is tight. 6. Set the string with the weights attached to the groove of the Atwood machine wheel, making sure that it is properly in place. 7.Then set the lighter mass on the appropriate demise of the machine, and hold in place, so that the starting point is at O degrees. 8. Make sure that the stopwatch is ready to start recording time. 9. When both the timer and the weight dropper are ready to start, exonerate the weight and start the time in sync with one another. 10. At the exact time the mass makes contact with the floor, stop the time as accurately and precise as possible. 1 1 . resound this process three times, so that an average can be obtained of the three run times, making the selective information a much more accurate representation of the time it takes he weight to hit the ground. 2. like a shot that the radius, masses, and time are recorded, it is time to perform 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 draw conclusions. Notes and Observations The Atwood machine contained four outer cylinders that stuck out of the wheel, which cause atmosphere resistance in rotation, and contribute to the moment of inertia. The timer, was hard to stop at the exact right time when the weight made contact with he floor.Lastly, there was friction of the string on the wheel, when the weight was released and it ru bbed on the wheel. Data kitty of the front weight 250 g=O. Keg Mass of the second weight eggs=O. Keg Weight 1=MGM= 2. 45 N Weight 2=MGM= 1. 96 N season 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 There was mistake to account for in this lab, which first started with the four cylinders that stuck out of the Atwood machine 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 total weight of the Atwood machine, because the wheel itself was massages in comparison.Even though it accounted for very smaller error in our experiment, it effected the other numbers that we calculated in our data, making them a diminished less accurate. When finding the amount of time it took the heavier weight to make contact with the rubber pad, there was compassionate 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 way of account 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 existed, 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 move in a circular motion. We measured many values, including the per iod, in order to determine the theoretical and observational forces acting on the pendulum. From this we were able to draw conclusions about how the experimental and theoretical forces relate to each other.We also were able to test Newtons second law of motion find out whether or not t holds to be true. The values that we obtained to get our experimental and theoretical forces started with setting 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 swinging 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 Just the string attached to the pendulum, we also measured the force gauge, because without it our reading s 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 beginning of the first crossbar and ended it at the same place.With these numbers that we measured we were able o calculate the angle 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 = 2/r to calculate 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 muffled down. From this we used Newtons famous second law, which was F=ma, to solve for the Force that was subjected on t he pendulum.We knew that if this value was airily constraining to our experimental value that his theory would be proven correct. Me modified the equation to fit for the situation that was involved, in which we used F = m x 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. round of the discrepancy in our data comes from the instability 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 pipe down when we set the pendulum in motion. We couldnt read exactly what was on the force gauge and it also kept ever-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 may 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 now 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, change our reaction time, and 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 experim ent 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 analogous 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.