October 3rd, 2016: LAB 9: Centripetal Force with a Motor

Michell Kuang
Lab Partners: Charles, Anthony
Date Performed: 10/03/16

In this experiment, we examined centripetal force by putting an object in circular motion using this apparatus:

Centripetal force apparatus with electric motor

There is a motor attached to the apparatus that puts the object in motion. By turning up the power of the motor, we increased the speed at which the object spun, which also increased the radius and angle. Our goal is to find a relationship between the angle theta and angular velocity.

To do this, we based our model off the equation:

ω^2=(gtanθ)/0.70+1.855sinθ

How we derived this equation is easier to understand if one looks at this diagram of the apparatus: 

Lab manual sheet with added labels and numerical data

As can be seen at the top of that sheet, the length L of the string can be separated into its x- and y- components, Lsinθ and Lcosθ, respectively. Lsinθ is going to be our R2, and Lcosθ is our H-h. Using this information, we can derive the equation.

Derivation of equation

Moving onto the experimental part of the lab, we took data for 6 runs at which the apparatus swung at 6 different speeds. We used a meter stick to measure our values for H and R. Our values for ω were obtained by timing how long it took for the object to make 10 rotations. For our h values, we put a piece of paper on a ring stand and slowly raised it until the object in motion hit it. Then, we moved that ring stand away from the spinning object, and measured the height h with a meter stick.

Data of 6 runs

After collecting all of this data, we put it into excel so we could calculate our theoretical values of ω and compare them with our experimental ones. 

Excel sheet of data

Our theoretical values turned out to be very close to the experimental values, with the % error being no more than 0.09%. Discrepancies in these values could possibly be from inaccurate readings of measurements such as H or from inexact timings of the time it took for the object to make 10 rotations. Although we can't really make our timing of the rotations more accurate, we can change our value of H on excel and see how that affects our data.

Excel sheet of data with modified H

Now, our  % error is no more than 0.06%! Regardless of this change, however, our initial values were accurate enough for us to confidently say that theta is, in fact, related to angular velocity as it is described in our equation.