Kevin Tran
Lab partners: Kevin Nguyen, Jose Rodriguez
1 April, 2017

Centripetal Acceleration vs. angular frequency

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

      Introduction: Our teacher used a rotational system to determine the centripetal force. The centripetal force is a force that allows a body to follow a curved path. We used the formula for centripetal to determine the centripetal force. With the rotational system, the professor will vary few things: the radius of the string, the mass of the object, and omega by changing the amount of power in the power supply.

Below is the force for centripetal force where:

F= Centripetal force

m= mass of object

r= radius

w= omega

In order to test this formula, we need to create several graphs.

Below is the rotational system we used to determine centripetal force.

1) First, we performed 5 trials when radius is varied, but everything else is constant. (data collected below).

With the collected data, we are able to construct a radius(x)/ force(y) graph that will give us mw^2 (slope), and we got it by linear fitting the graph. Our slope happens to be 6.930

2) Next, we performed 3 trials when mass is varied, but everything else is constant. (data collected below).

With the collected data, we are able to construct a mass(x)/ force(y) graph that will give us rw^2 (slope), and we got it by linear fitting the graph. Our slope happens to be 8.869.

3) Next, we performed 3 trials when omega is varied, but everything else is constant. (data provided below). All we were given is the change in the power supply, so we have to find omega.

Since 10 rotations = 10 revolutions, in order to find omega, we have to convert the 10 revolutions into rad/sec. (work shown above for each trial).

From the collected data, we are able to construct a omega^2 (x)/ Force(y) graph in order to find mr(slope), and find it by linear fitting the graph. As a result, the slope is 0.1078

4) Next, we made a mw^2(x)/ Force(y) graph. We used the same results from the previous data when omega is varied to make this graph. By creating a linear fit, we are able to find slope (r). Our slope (r) is 0.3667.

In this graph: 1) Mass is supposed to vary.

                        2) Omega wasn't supposed to vary

                        3) Radius was for sure constant

5) Next, we made a rw^2(x)/ Force(y) graph. We used the same results from the previous data when omega is varied to make this graph. By creating a linear fit, we are able to find slope (m). Our slope (m) is 0.2292

In this graph: 1) Radius is supposed to vary.

                        2) Omega wasn't supposed to vary.

                        3) Mass was for sure constant.

Conclusion: Overall, we were able to test for the formula F(Centripetal force)=mrw^2. What we noticed is when radius is increased, the average force for 10 rotations increases as well. Also, when mass is increased, the centripetal force increases, and the case is opposite when the mass is decreased. When our teacher increased the power supply, our omega increases as well. A problem that could of occurred during the lab is if we only collected data for 5 rotations instead of our usual 10 rotations. Also, another error that could happen is if we were to calculate everything in centimeters and grams, but our usual units is meters and kilograms. We were able to learn a lot about centripetal force, and we can use this knowledge to understand how everything around us works.