3-April-2017: Centripetal force with a motor

This time, we used another way to verify the function of centripetal force.

Purpose

By using the apparatus as following to find whether the angular speed also works on the function. 

Plan

1. Set up an apparatus as following. 
   
2. Through the diagram
   
   We can get the function 
   
   Then, it turns out to be 
   
3. Then, we can derive angular speed from measurements of R, L, H, and h to get r and tanθ. 
   
   
   
   
4. Though the function
   
   We can measure angular speed with a stopwatch. 
5. Compare calculated angular speed and actual angular speed (from the period). 
6. If the absolute value of calculated angular speed minus actual angular speed is smaller than the uncertainty, then the function is verified. 

Set up

Professor gave the apparatus as following. (And the diagram shows under.)

For the period, we used a stopwatch to measure 10 times period and then divided it by 10 to get the period. 

When we measure the h, we used a small piece of paper. 

Every time the small object passed through, we rose the paper until it hit the object. Then, we measure it by a ruler. (so as other measurements)

Then, we collected the data in different angular velocity as follow. 

Analyze

By the given information, we can calculate the angular speed is 

Uncertainty

By the function above, we can calculate the uncertainty of angular speed. 

After plugging into Excel, I got

Most data is in the range of uncertainty, which means the experiment works. 

Conclusion

From the uncertainty, we can say those data is acceptable. Therefore, we can say the centripetal force function

does work in the different situation.