September 29 2014: Angular speed for a particular rotating apparatus

Purpose: To find a relationship between angular speed(w) and angle created by the string relative to the vertical on a particular rotating apparatus.

This is the rotating apparatus that the class used to calculate the rotations and the time for this lab. There is a string attached to one of the ending of this apparatus, where a weight is located, and it was our reference.

First, we took some time to calculate the measurements of this apparatus such as height, length of each arm, length of the string, etc... Then we calculated the time of 10 rotation at 8 different speeds and we are going to attempt to find the angular speed for each trial by utilizing the given equations and using a computer to calculate the values for us.

This is the model that our professor drew on the board for us to use as reference of what measurements to take from the apparatus.

We drew our own model of the apparatus, and as possible to see, we have the measurements of each relevant part of the apparatus, and we are going to solve for h2, and theta according to each trial.

This is the picture of the values that we got for each of the eight different trials that the class did. Each time was taken for 10 rotations of the object.

 These equations were the ones that we found relevant to finding the angular speed for each trial. From those equations, we expected to get numbers to create a graph for the lab.

In order for us to perform the calculations easily, instead of finding each angular speed for each different trial by hand, we plugged the numbers in excel and created formulas to calculate the values faster.

This is a graph of w(rad/s) vs. f(theta). Our expectation was to get the slope close enough to 1, which would show that our calculations for the angular speed would be accurate, we got 0.9987, a number really close to 1.

Summary: First, we got the measurements of each relevant part of the rotating apparatus. Then the professor turned on the apparatus and we timed 8 different trials at different speeds. We drew a model of the apparatus with our measurements and tried to find a equation where the angular speed(w) would be a function of theta. We got w^2=g*tan(theta)/d+l*sin(theta) to be our equation. We used each different trial to get a different value of w, and we plugged those numbers in the computer. After that we used the equation w=2*pi/time to calculate the angular speed(w(rad/s)) relative to the time for each rotation. We also plugged this numbers in the computer and created a graph w(rad/s) vs. w=function of theta. The slope of that graph had to be close to 1 to indicate that our calculations were accurate, and we got 0.9987 which is considered close. This showed that our calculations/measurements were good.