3-Oct-2016: Centripetal Force with a Motor

Lab 9 Centripetal Force with a Motor
Date: 03 October 2016
Name: Andrew Martinez
Lab Partners: Richard Mendoza, Lynel Ornedo, Mohammed Karim

Statement: To determine the relationship between theta and omega.

Introduction: As angular speed increase due to the motor spin the mass shifts to a larger radius resulting in an increase in angle theta.

Apparatus:

An electric motor mounted on a surveying tripod. Long string tied to the end of the horizontal rod. Rubber stopper at the end of the string.

Long shaft going vertically up from shaft with a horizontal rod mounted on the vertical rod. Ring stand with a horizontal piece of paper on tape sticking out.

Procedure
- The professor has control over the motor and thus can increase it for the experiment.
- The students use the vertical stand that with the paper sticking out to find the mass height from the ground.
- Students are also responsible for measuring the amount of time it takes for the mass to make ten rotations
- Using all the measured data students can then conceptually break down the components of the centripetal force to derive an equation for omega
- Using your actual and calculated values one can then graph these omegas to how close the correlation is and the percent error to see if theta is related to omega.

Measured Data

Using our understanding of centripetal forces we are able to derive equations and variables based upon this understanding. Through this we can display the relationship between θ and ω.

On this page we derive several equations to help in proving the relationship between theta and omega. H is a constant as it stands for the vertical stands height. Little h is the shifting height of the swinging mass as the motor increases in speed. L is the length of the string and while the swinging mass may shift height L will always maintain its length. Knowing this we can find theta through SOH CAH TOA. Since only A(H-h) and H(L) are known we can use the arccosine to find theta. Since we know that omega is equal to theta divided by time we can find the actual omega.

In this picture we are trying to derive an equation to find omega by calculation and understanding of centripetal force. We break our net centripetal force into its X and Y components where Fx: Tsinθ=mrω^2, Fy: Tcosθ-mg=0. By setting T=mg/cosθ we can substitute into T to solve for omega as seen above where the masses cancel each other out, sin over cos can be changed into tan and r is r+Lsinθ to account for the changing radius.

 Graphing Analysis

By graphing our actual values of omega and the calculated value of omega and performing a linear fit with a correlation we can see that the correlation is .9999 almost at 1. 

Upon conducting a percent error test we can see that the actual and calculated values are reasonable close to each other and that by doing so we can see that their is a relationship between omega and theta.

 Conclusion: Based on our results we can conclude that there is a relationship between omega and theta. For as theta increase so did omega and that by deriving an equation for omega through trigonometry and using theta we were able to get accurate results for omega.  Based upon our low percent errors it is safe to presume that theta is related to omega. One concern that should be noted in the rising percent error as the values went further along. Some possibilities for this could be a random error of changing speed in the motor or a systematic error of timing of the rotations.