27-Mar-2017: Centripetal Acceleration vs. angular frequency

Since we knew the relationship between velocity and centripetal and the relationship between velocity and angular frequency, we can easily calculate out the relationship between angular frequency is

In today's lab, we set up some apparatus to measure whether the function fits for actual operation.

Purpose: To determine the relationship between centripetal force and angular speed. 

Set up:

This time professor brought a special disk that allowed a mass rotate on the top, while the wireless force sensor measuring the force, and photogate reading periods. 

Then, professor placed the different mass in the same distance from the center in the same speed. 

Next, professor placed the same mass in the different distance from the center in the same speed. 

Last, professor placed the same mass in the same distance from the center in the different speed. 

And we got the data as following. 

Analyze:

For the first set (constant r, omega), we got the relationship between force and mass as following.

It is easy to tell that they have a linear relationship, which is 

For the second set (constant m, omega), we got the relationship between force and mass as following. 

However, in the real material, we were failed to create the same omega, so we can only find out the relationship between centripetal force and (radius*omega^2). 

We can tell if the mass stays the same, there is a linear relationship between force and (radius*omega^2). (we can discover the relationship between force and Omega after analyzing the third set data.)

For the third set (constant m, r), we can figure out the relationship between force and omega. 

Then, there is a polynomial relationship between force and omega (which is power to 2). 

Conclusion:

Overall, we can tell the centripetal force has the linear relationship with mass, radius, and the square of angular acceleration. To sum up, we could get the function

which is exactly the same as what we got from the algebra. 

Uncertainty:

By the function, we can get the uncertainty function is

and

(because)

Then, we can calculate each uncertainty of value. 

For most data, they are in the range of uncertainty. However, the data of the second set, which has some problems with constant omega, has some problems with uncertainty.