Lab 8

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 7 September 2016 

Propagated Uncertainty in Measurements

Mission Statement:To verify the equation F = m*r*w^2

Theory: When an object moves in a circle at a constant speed its velocity (which is a vector) is constantly changing. Its velocity is changing not because the magnitude of the velocity is changing but because its direction is. This constantly changing velocity means that the object is accelerating (centripetal acceleration). If the object is accelerating, then it must be subject to some force.
Experimental Procedure:

 For this experiment, the procedure was rather straightforward, basically involving us spectate as the professor made use of a spinning-table mechanism (shown below) on which a block was tethered to the central rotating rod, and depending on the distance between the block and center of rotation, or depending on the weight of the block, or depending on the angular velocity of the rotation, different readings for the force would be recorded by us.

 The professor would conduct the experiment 10 different times, holding the mass constant for the first 8 times and the radius of rotation constant for the 5-10th trials. Together with the values for the force and time, we built a table in Excel calculating the angular velocity we reached, together with the quantities w^2, rw^2, mw^2, and mr shown below.

Next, we plotted the graphs of Force verses rw^2, Force verses mw^2, and Force verses w^2, whose slopes should yield m, r, and mr, respectively. The graphs are shown below.
Lists/Tables/Graphs of Collected Data with Explanation:

Graph of Force verses r*w^2
Below the slope is shown to be 0.2026, which corresponds nearly exactly with the weight of the block when the weight was held constant. 

 Graph of Force verses m*w^2
 Below the slope is shown to be 0.8249, which did not correspond very well with the radius of the block when the radius was held constant at 0.58 m. 

Graph of Force verses w^2
 In the graph below, the value of A is approximately equal to 0.1249, which is fairly close to our expected value of m*r = 0.116. 

Conclusion- The difference between our 'slope' values and their corresponding 'recorded' values, can best be attributed to poor timekeeping and insufficiently advanced equipment. The mechanism which spun the horizontal, circular table relied upon fixed wheels underneath the table to exert the spinning force, thereby increasing the number of places were the circular table touched another surface tand thereby experienced friction. I suppose if we had a mechanism in which the circular table connected directly with the rotating axle rod, there would be less friction and thus a more accurate reading of the angular velocity.