There are several measurements that we had to record in order to come to an educated conclusion for the relationship that we wanted to establish. First, we had to record the dimensions of the apparatus that we used so we could calculate the angle from its' central support to the line of string that was connected to the swinging object. For instance,we measured the height of the object from the floor, the radius of the extended arm, and length of the string that were all part of the apparatus so we could the formula angle= arccos(H-h/L) to calculate the angle per each trial. Second, we had to record approximately how much time the object would take to pass the same point ten times so we could calculate the angular speed by dividing 20(3.1459)/delta time of each trial to get the Omega for each trial. Last, we used the force diagram of the hanging object to get a formula that relates omega and angle.
To start this experiment, we had to measure the apparatus so we could have data to make certain calculations. We measured the height, the radius of the arm that extended out away from the shaft, and the length of the string and recorded the measurements. Then, the professor flipped the switch to the power source of the apparatus and the object began to swing in circles as we recorded the time it took the object to revolve around the same point ten times so we could calculate the angular speed per each trail. Once everyone had taken the needed measurements, the professor used a simple apparatus that indicated where the height of the object was per each trial so we could record the height of the object for each trial and use the information for the calculations for the angle per each trial. Last, we used the collected data to calculate the angle and omega and also to make a graph of the calculated omega vs. visualized omega.
This image shows the apparatus that was used for the experiment. It is built with a tri-pod stand, an electric green motor with a metal rod sticking out of it, a horizontal meter stick, and a hanging black object connected to a string that is connected to the meter stick.
This is a closer image of the apparatus.
This is an image of the data for the last two trials.
This is a further view of the graph just mentioned.
In conclusion, we did find some relationship between the angle and the angular speed of the swinging object. For instance, what we visualized vs. what we calculated with mathematical formulas and physic's knowledge did create a graph with almost 100% in correlation between the two which leads me to think that the approach we took to find the relationship was successful. The difference in the two angular speeds could have been due to several reasons. For example, the values for the rotations of the object in relationship to the metal frame that was used were calculated with our vision and the use of a wrist watch that I pressed for each trial's time interval. So there is likely some calculation error for the time interval that translated down the physical calculations. Also, the way we measured little (h) for each trial was not accurate at all because we just eyeballed the height every trial and measured it with an old meter stick that had worn out number units that had hard to see values. Lastly, the apparatus itself was not precise for each trial because it was built unstable. For instance, the motor was taped on to the tri-pod and the me tri-pod itself was not completely vertical for each trial which also lead to errors in the mathematical calculations. Hence, there were many reasons why the calculated values for the angular speeds were different but I think we did show that there is a relationship between the two because the values were close to one another and because the graph gave the value of 0.9935.
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