Lab 18: Lab Problem – Moment of inertia and frictional torque

Lab 18: Lab Problem – Moment of inertia and frictional torque

Authors: Mohammed Karim, Bemaya, and Louis.

Objective: Find the frictional torque done by the wheel and determine the time it would take for a car tied to the wheel to slide down the track.

Theory/Intro: We understand that inertia acts as a system and, as a result, can ratio the values to find the mass and inertias of each individual object.

Apparatus/Procedure:

              

Pic of apparatus

               In this lab, we are given a metal disk that spins on a shaft and are tasked with making measurements of each of the parts. We then calculated the volume of each individual “cylinder” and used proportions to find the mass of the disk and the supports. (See Figure 18.1) Then, we recorded the spinning and marked it using LoggerPro to find the deceleration. This value, the angular deceleration due to friction, was 0.5551 rad/s^2. We then calculated the torque due to friction (See Figure 18.2) Now that we had the frictional values, we could run the car down the 1 meter track. We set up a sum of force equation and concluded that the car would have an acceleration of 0.0333 meters/second^2. Finally, by using kinematics, our theoretical time for the time it would take the car to travel 1 meter was 7.76s. (See Figure 18.3) After running the experiment, our experimental value was a bit lower than our theoretical value, but by less than 4%.

Data Tables/Analysis:

Figure 18.1 - Calculation for the mass of the metal disk and the torque due to friction

Figure 18.2 - Value for frictional deceleration (off by a factor of 10; did not do meters)

Figure 18.3 - Calculations for the time it would take the cart to travel 1 meter

Conclusion: This lab, being a giant problem, is basically a two part question, in which first you must find the frictional torque behind the spinning of the wheel, then you must use it to calculate the acceleration of the car and, as a result, the time it takes the car to travel one meter. Overall, our theoretical value was very close to our experimental value, but could be off due to the uncertainty of our calculations, the uncertainty behind the ratios of mass to volume, the uncertainty behind the angle the track makes with the horizontal, and the fact that we neglected the friction due to the track and the car. However, if these values were considered, we would have seen a far more precise answer.