Sept-23-2014 A spinning mass and its relationship to an angle

Purpose:
In this lab students will devise a relationship between angular velocity and an angle created, use that to calculate angular velocity and compare that with the actual angular velocity.

Lab:

The Professor sets up a motor powered contraption that spins a stick around with a string and a mass tied to the end of the stick. As the stick spins faster the mass gains velocity and spins at a taller height, while the angle between the string and the stick decreases.

Setup:

Students will start by measure the height of the stick off the ground, the length of the stick, and the length of the string.

The Professor will then set the motor to spin at a certain constant velocity and the mass on the string will rotate at a set height. Students will then measure the height the mass reaches. And also record the time the mass takes to complete 5 rotations.

Measuring the height of spinning mass:

This process was repeated a total of seven times with each repetition at a higher velocity and height.

After the data was recorded, the students then drew a model of the apparatus to find a relationship between the speed of the stick and the angle created between the string and the stick.

Model: 

The students then used this model to come up with a relationship between the angular velocity of the stick and the angle between the string and the vertical line from the tip of the stick to the ground.

The formula the students came up with was 

The students then set out to confirm their formula by comparing it to the formula w = 2pi/T.

The students used excel to find the numerical values needed.

Excel plot:

They then plotted a graph of the w found from the students equation and w found from w=2pi/T.

The students expected the graph to have a 1 to 1 relationship and therefore the slope to be 1, but that was not the case. Clearly something was wrong with the data or calculations.

The students conjecture the calculations may have been off for the formula relating w to theta. Or the data collection of the period may have been incorrect.