PHYS 4A/ Fall 2014; Relationship Between Angular Speed and Angle of Rotation

Purpose: To find a relationship between the angular velocity of an object and the angle it is rotating at.

In this experiment, a contraption was created so that a motor spun a wooden stick in a circular motion. A string and rubber stopper were attached to one end in order to measure conical motion. An electric generator was used to power the motor at a constant rate so that we could control the rate at which the conical pendulum rotated. 

Before beginning the experiment, certain dimensions were taken for calculations that would take place during the analysis. The total height of the contraption was measured to be 2.088 meters. The length of the string was 1.654 meters. 

Once the pendulum began spinning and reached an equilibrium, everyone recorded period values using their phones or stopwatches. Then a metal rod with a piece of paper was used to give a reference for the height of the rubber stopper above the ground. The paper was either higher or lower depending on where the rubber seemed to pass at any given point. Once the stopper skimmed the paper, the height from the tip of the paper to the ground was measured. This was done 8 different times in order to get 8 different angular velocities and heights.

Once the experiment was over, the data was analyzed using excel. Using trigonometry, the angle of the string was determined from the values of vertical distance from the top of the pendulum to the rubber stopper and the length of the string. These were values were compared using inverse cosine in order to get an angle. This angle was converted to radians and used for calculating the angular velocity. Both experimental and theoretical angular velocities were calculated. The theoretical and experimental angular velocities were calculated using the equations below. 

r = radius of the wooden stick

l = length of the string

Using these equations, theoretical and experimental omegas were calculated as follows.

The experimental and theoretical values were then graphed against each other in order to determine a percent difference.

As you can see in the graph above, the slope was 1.0384. This shows that the angular velocity had definitely increased in each trial. It also states that were were about 4% off from theoretical values since it is not increasing exactly proportional. This is due to the amount of uncertainty from taking the height of the rubber stopper as it was not exactly consistent as well as the measuring of the periods. Overall, the experiment showed that as the omega increases, the angle also increases as the tangential velocity will increase thus pulling the string more horizontally.