Lab 9: Centripetal force with a motor; Lab Partner: Jamie Lopez; 10-09-2016

2) In this experiment, we will accomplish to show the relationship between angular velocity(ω) and theta(Ө) when an object rotates in centripetal motion.

3) In order to find the relationship between the angular velocity and theta, we first have to find what is rotating in centripetal motion. In this experiment, we will have a mass pulled by a string in rotation. We know that the sum of forces is equal to mass and acceleration or mass times radius times angular velocity square. Drawing a free body diagram gives a better demonstration of the external forces acting on the object. We separate the sum of forces into x and y components to where sine and cosine represents Ө into the equation. Here is a picture with a better illustration of finding the relationship between the angular velocity and theta.. Now this relationship only applies when the angular velocity remains constant over time.

4) We will be using an apparatus to find the angular velocity in two methods. Finding ω by theta by imputing it in the equation and by time for using a stop watch for every rotation the mass passes by. Here's a picture of the apparatus for a better visual.
First, we will use the formula and input Ө by solving using the Pythagorean Theorem between the height of the apparatus, height of the mass above ground, and the length of the string attached to the mass. . In this result, we notice as theta increases, the magnitude of the angular velocity and the height of the mass above the ground increases.

5) After finish recording the experiment and imputing the data and values, here are the results we find using the equations between theta and ω and theta and time.  In the second picture, the angular velocity is equal theta over time. So every time the mass rotates in full 360 rotation, that would be our marking point of how long the mass takes to rotate in one revolution. These two equations we're representing of solving ω by theta and time should equal each other. But of course, there is an uncertainty error in the time equation due to human error.

6)

7) Technically, the graph should be similar to each other of the data points. The results we got are pretty close to each other. It's off around 6%.  The x-axis is theta we measured in the experiment. The y-axis are the equations we input using theta.

8) This is the proof of the relationship between the angular velocity and theta. As the angel theta increases over time, the angular velocity increases its rate over time; assuming it remains constant.