23-Sept-2014: Relationship Between Angular Velocity and Angle Lab

In this experiment we analyzed the relationship between angular speed and the angle of which a hanging mass makes with the vertical axis.

To see this relationship we used a tripod, electric motor, a rod, a hanging mass, a metal stand, a stopwatch, and something measure the height of the setup.

The motor was attached to the top of the tripod so that its spinning wheel was horizontal. The rod was then balanced and attached to the wheel of the motor. Using some length of string a mass was hung from one end of the rod. Once the motor was turned on, the rod would spin and the hanging mass would swing out some angle away from its original vertical position. To analyze the relation between angular velocity and the angle at which the mass would swing out once spinning we ran various trials at different speeds by adjusting the motors output.

Once spinning, as previously described, the hanging mass would swing outward and now its height from the ground would change. While it would be difficult to measure the angle at which the hanging mass moves to, its height relative to the ground would be fairly easy. For this part we used the vertical metal stand  with a horizontal rod, whose height may be adjusted, mounted to the vertical rod and a sheet of paper mounted to the end of the horizontal rod. When the system is spinning at what seems like a constant angular velocity we began to record the time it took for the system to make 10 full cycles using our stopwatches. The it took divided by the 10 cycles would give us the period, T, which we used to calculate angular velocity, w.

T = (time for 10 cycles)/(10 cycles)

w = (2pi)/T

While still spinning we cautiously began to move the metal stand closer to the proximity of the hanging mass making sure that the horizontal rod with the paper attached is still below the hanging mass. Once near, we once again cautiously adjusted the height of the horizontal rod until the paper was just grazed by the hanging mass. We repeated this process for several trials and with each trial we increased the power to the motor which gave us a faster angular velocity, a smaller period, and a larger angle. Below you can see a simple sketch of the entire setup which also labels the various lengths we had to measure.

Angle = arcsin [sqrt((L)^2 - (H-h)^2)]/(L)

Below is the data we collected during 7 trials. The data is labeled at the top of each column: period, height, angular velocity (measured), angle, radius, angular velocity (squared), and our calculated angular velocity.

The data from the calculated and measured angular velocity was then plotted as seen below. While our plot seems to be a bit scattered when we fit it linearly we see a constant slope that closely describes a relationship.