September 28, 2016: Centripetal Acceleration vs. Angular Frequency

Anthony Betancourt
Lab Partner: Josh Fofrich
Professor Wolf

Lab #8: Centripetal Acceleration vs. Angular Frequency

Purpose:

The main objective is this lab is to establish a relationship with the centripetal acceleration creating from a large turntable and the angular frequency that it experiences .  Gathering enough data from the time it takes to complete 10 rotations, measurements from power supply source, and calculating various rotational speeds are all methods involved in this lab.

Procedure:

1. Turn on power supply to the turntable to 6.4v.  Once turntable is on allow it to achieve a constant speed until taking measurements. Use 200 g mass on turn table
2. Once table speed has stabilized, allow lab pro to gather data from photo gate and accelerometer.  
3. After timing 10 rotations, move accelerometer to a different distance from the center of rotation.  
4. Gather data from new radius and repeat until 4 trials have been completed at this voltage.  
5. Apply a voltage of 7 volts to turntable using the same 200 g mass at a radius of 58 cm. Record  time for 10 rotations and record mean value on graph.  
6. Apply 7.3 volts to table and record time for 10 rotations as well as mean value on graph.  Use same radius as step 5.
7. Apply 7.6 volts to turn table and record time for 10 rotations as well as mean value on graph.  Use same radius as in step 5.  
8. Next three trials will use a radius of 58cm, 7.3 volts, and only change the mass used. Use masses of 200g, 100g, and 50g.  Record time for 10 rotations and mean value from graph.  

Theory:

To find the relationship between the centripetal acceleration and angular frequency, we make sure the table is spinning at a constant speed by reading a value of zero in the x direction from the accelerometer. Then we vary the masses attached at the end of the accelerometer in various radiuses from the center.  This is done to record any changes in the angular speed as the mass is moved out further from the center as well as observing the changing of different masses effecting the angular speed and centripetal acceleration.  If the apparatus is a perfect representation of the relationship between angular speed and centripetal acceleration, the outcome should be a correlation of one on a angular speed squared vs. acceleration graph.

Measured Data:

(turntable apparatus)

(close up of accelerometer and mass)

(calculations for omega)

(table of gathered data)

(graph showing Force vs. Radius*w^2)

(graph showing Force vs. Mass*Radius)

(graph showing Acceleration vs. Angular speed^2)     

Analysis:

The first two graphs have a correlation value that is within the accepted value.  The data collected from the lab demonstration proved to be reliable.  The graph depicting Force vs. Radius*w^2 has a correlation value of 0.9996 which can almost accurately predict the amount of mass used in the system.  The graph showing Force vs. Mass*Radius has a correlation value of 0.8909 which can still be used to calculate the angular speed of the system given a mass and radius of the circle, but unfortunately only to a certain degree of accuracy.  The last graph shows the the centripetal acceleration vs. w^2 with a slope of 0.8932 which can be used to predict, to a certain degree of accuracy, the value for the force acting in the system.  Some uncertainties may be a result of the unstable turn table apparatus and possibly the power supply to the motor turning the table being able to provide a steady rate. 

Conclusion:

The experiment provided some exceptional data for student evaluation.  Although some kinks need to be sorted out with the apparatus, the overall experiment went better than expected.  With some adjustment to the turntable, the experiment will be a great learning tool in this subject of angular speed and centripetal acceleration.   The data is accurate enough to reproduce any future experiments with very little uncertainty.