Lab 4_ Rotation

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Feb 20, 2024

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Lab Report 4: Rotation Names Percent Zoë Howard 100% Q1) In this experiment, the goal is to balance a couple of the weights by keeping the rod and the fulcrum where they are. Get the simulation from here. This video highlights the free body diagram, identifies the torques, and how you can proceed in general. In the simulation, drag and drop a couple of weights on the horizontal ramp so the system is at equilibrium. Prove that the equilibrium is reached with calculations (show your work). ???? ?? ?ℎ? ?????? = 0. 25?? ???? ?? ?ℎ? ????𝑖??? ????????? = 0. 626?? ?1 + ?2 = 0 (????? ? ?𝑖?????? ?? ?ℎ? ?????? ?? ?????𝑖??) 1 + (????? ? ?𝑖?????? ?? ?ℎ? ??????) 2 = 0 ???𝑖?𝑖?𝑖??? ?????𝑖??: − (4. 21 ? 1. 25) + (7. 27? 28. 8) = 0 _____________________________________________________________________________ Q2) A solid disk is mounted on a contraption with a spinning axis. Take another solid disk and place it on top and in the center of the contraption with the metal hoop. We make sure to apply the same torque to both contraptions . Watch the experiment in the video here. Which contraption spins faster, and why? Explain . Answer: The contraption that spins faster is without a doubt the one with the metal loop. This is because the contraption has a weight on it which makes it turn faster. The heavy parts of the systems are far away from the axis of the intended rotation. This means the greater the moment of inertia, the harder it becomes for the system to spin, making it faster within a specific direction. This is also true in terms of why the metal loop contraption spins faster and longer than the non-metal loop because there is more force and mass involved during the spinning cycle. _____________________________________________________________________________

Q3a) Let the rod swing from its end and from 90° with the vertical. Note the time with maximum angular acceleration and speed occur. Explain. ???𝑖??? ??????? ?????????𝑖??: − 2. 2????/? 2 ???𝑖??? ??????? ?????: − 2. 4???/? ?𝑖?? = 3. 22???? As the rod swings a few times, it can be observed that the maximum angular acceleration and speed do not stay constant, however, it is only when the rod gets enough rotational speed that it reaches this climax value. This can be the case because the mass is not at equilibrium meaning one side of the rod has more mass than the other affecting the gravitational acceleration and pull it has. _____________________________________________________________________________ Q3b) Now mount the rod a bit toward its center of mass and repeat the measurements of the previous question. Explain. ???𝑖??? ??????? ?????????𝑖??: − 2. 76????/? 2 ???𝑖??? ??????? ?????: − 2. 4????/? ?𝑖?? = 3. 62???? As the rod swings a few times, it can be observed that the maximum angular acceleration and speed does stay constant, this can be the case because the mass is in the center which means the rotational speed is always at max value. ____________________________________________________________________________ Q3c) Compare and explain the similarities and differences between the two experiments. Answer: Some similarities between the two experiments are that the time stamps are ranging around the same time. This can be because it doesn’t take long for identification of the maximum angular acceleration and speed to run its course and to be identified. It almost makes me feel as though this is true for many other similar objects because the maximum is the highest threshold the object is capable of. Another similarity is the values are both negative and have similar values as well. I think this is because both experiments started off at the same origin

times which was (0.00secs). Differences are of course where the place of the rod is and what direction it falls to first. I also think it is important to stress that both experiments were different when it came to the placement of the mass. This mass distribution could cater a lot to why the rod decided to fall in either direction first. _____________________________________________________________________________ Q4a) Is it rotating faster or slower? Explain this observation in terms of internal torques [Hint: see eq. (5); if the angular momentum is conserved before and after the placement of the extra disk, then before =after). Answer: When the disk is spinning and the hoop is placed on top disturbing the disk’s rotation, the system slows down before it abrupts the cycle and comes to a complete halt. While you can always conclude that the object has some time of internal forces that ultimately affect the system, the forces that contribute to this change can possibly create a torque which means there will always be additional forces that create some type of opposite torque as a result. ________________________________________________________________________ Q4b) Why can we claim that the conservation of angular momentum applies to the system? Answer: We can claim that the conservation of angular momentum applies to the system because, within the realm of the physics world, angular momentum is characterized as being one of the focal points within the laws of conservation. This principle is a summation that goes in-depth about specific properties within a physical system that are deemed constant even further speaking when the system finds itself to evolve progressively over time. This means the system will remain the same even after an external force is applied. Further speaking, momentum is described to be a vector quality. This provides an explanation explaining why the use of vector addition helps to connect and sum up the momenta that is encompassed and makes up the system as a whole. Considering these two main factors we can better understand, for example, why a system of two similar objects can still have equal speed although they are moving away from one another in opposite directions. This helps prove this claim because since the opposite vectors cancel each other out, the momentum within the system can remain zero, even though the objects are moving.

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_______________________________________________________________________ Q5a) Are your expectations met? (i.e., does the ball do what you’d expect?) Answer: Yes, after watching the Simphy experiment, my expectations of what the ball would do were met. This is true due to my knowledge of being aware that when a ball is dropped, gravity pulls the ball toward the ground due to automatic resistance after being in the air. The result of this is that gravity slowly stunts the travel time of the ball, and the bounce becomes shorter and shorter until the ball stops bouncing altogether. _____________________________________________________________________________ Q5b) If your expectations are not met, can you play detective in Simphy and find the reason? How is this related to the torques and angular momentum? Explain. Answer: To be more precise, I thought the Simphy experiment was meeting my expectations however it feels a bit incomplete now that I am reviewing it for the fourth time. From just glancing at it, the experiment looked to be something that seemed fairly correct because it was short and concise. The biggest thing is friction and resistance were the reasons why these expectations were not met. However, this doesn’t explain much of anything if I am being honest. Not sure if a positive external torque is taken into consideration, examples would be wind and gas, but it feels a bit unrealistic. Also, the only thing that is prefaced and values are given for is time and angular momentum. The angular momentum values seem to close in number as well given that shifted its speed once it had an impact with the ground. _____________________________________________________________________________ Q5c) What can you change in the simulation so your expectations are indeed met? How is this related to the torques and angular momentum? Explain. Answer: To relate this stimulation more in terms of the torques and angular momentum factor, I would stress more detail so the viewer and even experimenter isn’t in the dark about initial/final speed, force, and the difference in angular momentum from before and after it makes an impact with the ground. Of course, there are other factors as well that need to be expressed however the

main point is to just be specific about every occurrence that is happening especially the torque and angular momentum because they cater to distance and the turning that is occurring in relation to the object. _____________________________________________________________________________ Q5d) In light of the experiment's results above, can you now justify why the fidget spinner with more mass away from its center will spin longer? Answer: The fidget spinner with more mass away from its center will spin longer because what occurs during this process is the spin time decreases and the terminal angular velocity increases. This is because the mass that is added ultimately causes the moment of inertia to increase as well. All in all, the moment of inertia acts as an aid to measure the object’s resistance to changes within its rotational rate. To put it simply, the larger the moment of inertia, the longer the object will spin while also providing a faster angular velocity. This concludes the notion that angular momentum will affect the angular velocity due to added mass. Not only is mass affected, but so is the distribution of the mass. Being able to control the adjustable spokes on the fidget spinner allows the mass to be more at a fluctuating speed, meaning the angular velocity, again is affected and can be altered. Changing this distribution of by adding more, changes the object's overall moment of inertia which determines proceeding factors such as angular momentum, angular kinetic energy, and of course angular velocity! _____________________________________________________________________________ Q6a) Run the simulation and, based on the conservation of energy concept, solve for the landing speed of the weight [you did the same thing in the previous lab]. ?????𝑖?? ? = 2. 67 ? 10 −6 ?/? ????? = 0. 80? ??𝑖?ℎ? = 6. 25? 𝐾?: ℎ = 1 2 ?? 2 ?? = ?𝑖 + ?? 6.25? 5 = 5? 2 5 ?? = 0 − 10(1. 06) ? = 1. 06??? ?? =− 10. 6 / ?? = 10. 6 ?/? _____________________________________________________________________________

Q6b) Without including any friction or changing the objects’ masses, is there anything we can do to lower the weight's landing speed? [Hint: Maybe the moment of inertia of the pulley?] Answer: Yes to sum it up, there is in fact something that can be done in order to make the landing speed of the weight lower. How it works will be in terms of the moment of inertia. As expressed in Question #5d, the moment of inertia changes in its rotational motion. This is determined by how far each mass is from its center. In terms of the moment of inertia of the pulley, this helped cater to reducing the weight of the load or even create needed energy in order to make it easier to light the load. Changing the direction of the force and even the energy required is the same regardless of whether the load is lifted with or without the pulley system. In addition to this, pulleys can reduce the acceleration forces that are required to lift, but this doesn’t change the amount of work that is done beforehand. Overall, I feel as though this is needed because it allows for the force of gravity to be implemented and lift things upwards. _____________________________________________________________________________ Q6c) Re-solve the conservation of energy, taking into account your previous findings [i.e., the rotational energy of the pulley], and collaborate on the new (lower) landing speed. 𝐾𝑖 + ?𝑖 = 𝐾? + ?? 𝐾 = ?𝑖???𝑖? ?????? 𝑃 = ??????𝑖?? ?????? ?????𝑖?? = 20. 09?/? ????𝑖?? ???????? = 9. 8?/? ???? = 0. 785?? ???. ????? = 2. 77? ??𝑖?𝑖?? ????? = 0. 00? ?𝑖??? ????? = 0. 80? ????? = 0. 209 ???𝑖???

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Lab 4_ Rotation

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