LAB 9 - Centripetal Force with a Motor
Tony Wu, Isaiah Hernandez
October 13, 2016
Experimental Procedure: We start off by setting the motor to an arbitrary speed, slow at first. We track the time it takes for the mass to make 10 revolutions. We determine the height that the mass is from the ground (h) by placing a stand with a small piece of paper close to the where the mass is rotating. Once the mass clips the paper, we record that as h. We are not able to measure the angle theta but we can calculate it using theta = cos-1[(H-h)/L]. The lab is recording the different values of the period T (seconds/revolution) as we increase the speed of the motor. Omega = 2π/T.
Data and Calculations:
Below is the the omega values that we timed, which we got from the equation Omega = 2π/T.
The calculated values are the values we got from our equation that relates H, h, L, R, and theta to omega.
Conclusions: As you can see, the values of omega_timed are all generally close to the values of omega_calculated. The values are all on average within 5% of each other. The slower speeds, speeds 1-3, all were closer in value than the higher speeds, speeds 4-6. This is likely due to user error, inaccurate estimates of the initial recorded rotations and/or rounding calculation errors. Nonetheless, the derived equation that relates omega and theta is a good estimate.
Lab Goal: To observe a spinning mass in order to determine the relationship between an angle theta and angular speed omega. Theta is the angle that a string makes with the vertical as the mass rotates around a central axis.
Theory/Introduction: A mass is hanging from a rod that is rotated around a central axis by a motor. In this lab, we vary the speed at which the motor rotates the rod. The angle theta is the angle that the string makes with the vertical as the mass rotates. The quicker the rod rotates, the greater the angle theta. We also observe the height h that the mass reaches as it spins. The greater the angle theta, the greater the height h. Three constants that we take note of are height H, the top of the string that is attached to the rotating rod, length R, the length of the rotating rod, and the string length L which the mass is attached to.
The overall idea is that given all the variables, we can determine the a relationship between how a change in the angular speed, omega would affect the angle theta, and vice versa.
Apparatus:
Theory/Introduction: A mass is hanging from a rod that is rotated around a central axis by a motor. In this lab, we vary the speed at which the motor rotates the rod. The angle theta is the angle that the string makes with the vertical as the mass rotates. The quicker the rod rotates, the greater the angle theta. We also observe the height h that the mass reaches as it spins. The greater the angle theta, the greater the height h. Three constants that we take note of are height H, the top of the string that is attached to the rotating rod, length R, the length of the rotating rod, and the string length L which the mass is attached to.
The overall idea is that given all the variables, we can determine the a relationship between how a change in the angular speed, omega would affect the angle theta, and vice versa.
Apparatus:
Experimental Procedure: We start off by setting the motor to an arbitrary speed, slow at first. We track the time it takes for the mass to make 10 revolutions. We determine the height that the mass is from the ground (h) by placing a stand with a small piece of paper close to the where the mass is rotating. Once the mass clips the paper, we record that as h. We are not able to measure the angle theta but we can calculate it using theta = cos-1[(H-h)/L]. The lab is recording the different values of the period T (seconds/revolution) as we increase the speed of the motor. Omega = 2π/T.
Data and Calculations:
Recorded Data for Total Time for 10 rotations, Period T in seconds/rotation and Height h in cm.
Freebody Diagram for the Hanging Mass
Calculations that relate theta to omega
Below are the calculations where we plug in values for theta, R, L, and H.
The only variable left in the equation is h which we will plug in from our recorded data earlier.
The calculated values are the values we got from our equation that relates H, h, L, R, and theta to omega.
Correlation of omega_timed vs. omega_predicted (omega_calculated)
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