April 5: Lab 9 Centripetal Force with a Motor

Lab 9

Centripetal Force with a Motor

Ricardo Gonzalez 

Josue Luna

April 5, 2017

The overarching goal of this lab is to understand there is a relationship between the angle of a horizontally spinning apparatus and the angular speed applied to the apparatus.

1. Theory
To understand the concept of this lab much easier. When we were kids, well atleast when i was, we have had some object attached to a sting and spun over our head horizontally. When we applied a larger force, the apparent  speed of the object increased and we observed the object was getting closer to moving directly horizontally to the pivot point. Similar to what we have done as kids, we can use an apparatus to apply an ever increasing force to create a larger angular speed and likewise, we will see the pivot angle will increase.

2. Procedure
We set up an apparatus in which a tripod will hold a motor on top. The motor is attached to a vertical rod that will spin as the motor is spun. A horizontal rod is attached to a vertical rod, and a string is attached to the horizontal rod. At the other end of the string we have attached a mass of m.

To conduct the experiment, we were to find the measurements needed from the apparatus. These measurements include the radius from the horizontal distance to the attachment point of the string, the height to the horizontal rod, the height to the bottom of the mass, and the length (L) of the string to the bottom of the mass. 

3. Measured Data

Radius (R) = 0.75 m

Sting Length (L)= 1.595 m
Height of apparatus (H)= 1.795 m
height to the bottom of mass (h)=  0.20 m

In order to find the Theoretical angular speed by only utilizing the measurements found for each trial, we will use the sum of the forces in the x and y directions. What we derived is an equation that is the equal to the angular speed W. 

To find the angle that the mass creates from the pivot point can be found using the laws of cosine. 

4. Results 

Our Measurements for each trial along with the calculated results for the angle, experimental and theoretical values of omega (angular speed).

A graph that shows the relationship between omega vs Theta (Angular speed vs Angle)

5. Analysis
By analyzing our data in the table shown above, we can assume the experiment was not perfect, as we can see the experimental and theoretical values for angular speed begin to deviate from each other more and more as the power is increased to spin the object. When we look at the graph of the omega vs theta, we can see that the line created is not linear. in fact, when we took an polynomial fit to the second degree, we can safely assume that as the angular speed continues to increase, the angle will even out and stay constant. Theoretically, we know it is impossible to increase the angular speed to the point where the mass will now move any higher than the pivot point, therefore the graph shown is correct in our representation of the angular speed vs the angle created.

6. Conclusion
In conclusion, we know the apparatus is not by any means ideal. Therefore, we can safely assume there is some friction created by the system that increases as the force to increase angular speed increases causing a reasonable deviation from our experimental and theoretical value of angular speed. As far as our graph that creates a relationship between angular speed and the angle created by the system, we can see that physics has not changed. As the angular speed increases, the maximum angle created by the system becomes harder to achieve. Therefore a larger angular speed is needed for the system to be perfectly horizontal.