Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
8 April, 2017

Centripetal force with a motor

     Purpose: Students will come up with a solution to find the relationship between θ and omega.

    Theory: We will be using an apparatus to find the relationship between  θ and omega. (picture shown below). As the motor spins at a higher angular speed (w), the mass revolves around the central shaft at a larger radius and the angle θ increases.

Below is the apparatus that we used to determine our values.

Below is the apparatus that is set up in order to find our individual values.

W= omega

R= radius 

H= height of the entire apparatus

h= height of the mini apparatus

L= length of the string

H-h= the height of the string when angled

Lsin θ= distance from the edge of the pole to the mini apparatus

θ= angle when angular speed is changing.

After measuring:

W: (listed below)

R= 0.8m

H= 1.8m

h= (listed below)

L= 1.61m

H-h= (listed below)

θ= (listed below)

1st, our professor activated the apparatus and performed 5 trials. Each trial represents a different omega.

Trials:

10 rotations x 2pi/time= rad/sec

1: 1.9 rad/sec (10 rotations in 33 seconds)

2: 2.3 rad/sec (10 rotations in 27 seconds)

3: 2.62 rad/sec (10 rotations in 24 seconds)

4: 3.14 rad/sec (10 rotations in 20 seconds)

5: 4.19 rad/sec (10 rotations in 15 seconds)

Next: We adjusted the height of mini apparatus to find the height of where the end of the string hits the paper.

As a result for a each angular speed:

Trials: (height)

1. 0.36m

2. 0.652m

3. 0.87m

4. 1.134m

5. 1.36m

Results of H-h:

1. 1.44m

2. 1.148m

3. 0.93m

4. 0.666m

5. 0.44m

Below is the equation created to find the individual angles of the 5 trials and the results:

Next, we created a formula to assume the angular velocity of each of the 5 trials

Below is the results of the 5 trials.

We compared the calculated omega with the omega given to us. While we have calculated omega(x-axis) and recorded omega(y-axis). As a result, the slope gives us a number of 1.136, which is really close to 1. This proves that our calculated result is close to the recorded. 

Conclusion: By comparing our calculated results with the recorded, the angular speeds of the 5 trials are almost similar but very close. It is true that the higher the angular speed, the bigger the angle θ will be.