01-April-2015: Centripetal force with a motor

Purpose: We will need to understand and develop a relationship between θ and ω. A model for ω will be formulated and compared to a measured ω.

Our apparatus for this experiment consist of an electric motor mounted on a surveying tripod, a long shaft going vertically up from the shaft, a horizontal rod mounted on the vertical rod, a long string tied to the end of the horizontal rod, a rubber stopper at the end of the string, and a ring stand with a horizontal piece of paper. 

For this experiment we recorded data relevant to our needs to solve our unknown values. We measured the height from the ground to the top of the vertical rod, the length of the horizontal rod mounted on the vertical rod, and the length of the string attached to the rubber stopper. 

This apparatus will spin at a certain voltage. As it is spinning the rubber stopper will hit the ring stand with a horizontal piece of paper. This will give us the height from the ground to the stopper. We repeat this six times, each time at a higher voltage. Also as is it spinning for each voltage we timed how many times the device went ten revolutions, so that we could get an average time for a single period.

As the apparatus spins it will create an angle and speed. Each time the voltage is increased the angle and speed will change.

-With these measured values we will solve for θ and ω. 
-As well as develop a model that we can use to determine ω.


To develop a model for ω we begin with a free body diagram of the rubber stopper.
Next we summed the forces and determine what our radius is, solving for ω.

The measured values we inputted onto excel and used it to calculated the θ and ω. The model values are also in excel.

The measured ω is 2 pi over our period of one revolution.

For the angle we inputted this formula for column E.








Lastly we graphed a measured ω vs. a model ω to determine if the model is correct.

Conclusion:  The angle is found by the length of the string and the height from the ground the rubber stopper is at that moment. The angle will assist us in finding the ω at that moment. If the angle is at a larger degree the ω will in turn become larger. 
For the measured ω vs. model ω graph if the slope is one we know that our model is correct (in a perfect world). Given that we measured lengths and heights those measurement have uncertainty. We also timed the periods with a stop watch using our eyes. Those two measurements will yield slight errors. Which is why in our graph the slope is not one. We were off by the hundredth decimal point, which is not bad. If the slope was significantly off we would know something went wrong.