Daniel Guzman
Physics 4A.
Moment of inertia and frictional torque
Purpose: The purpose of this lab is to determine the moment of inertia of a pulley, to then predict the time it would take a car that is attached to the pulley to travel down an incline that is a meter long and inclined at a certain angle.
The theory introduction: the theory for this lab is very interesting due that it uses different important concepts that are all linked to get to the desired result. The first important part of this experiment is to determine the moment of inertia of the pulley, the moment of inertia of the pulley is determined due that it is going to be used to determine the frictional torque of the pulley as it spins when it has the car attached to it, nevertheless the angular acceleration of the pulley has to be found first in order to determine the rotational torque of the pulley. After the frictional toque is determined using two important concepts such as the moment of inertia and and angular acceleration one will be able to find the time it takes the car to travel down the slope by using the concept of torque. Once the equations for torque are derived correctly one wants to find the tangential acceleration of the system to then use it to find the time it takes the car to travel down the slope.
Description of the apparatus: The apparatus for this experiment consisted of a laptop a big pulley, a car, a ramp, digital calibers and a phone. The laptop is used in this experiment to analyze the video that is recorded using the phone as the pulley spins in order to determine the angular acceleration of the pulley, the pulley in this experiment is a really important piece of the apparatus due that it plays a big role when determining the tangential acceleration of the system, the digital calibers are used to measure the dimensions of the pulley which are very important to determine the moment of inertia of it and the phone is used to measure the angle at which the car will be descending and the time it will take the car to descend a meter. The experimental set of the apparatus is quite simple due that it only requires one to attached a string to the car and the pullet and set up a ramp at a certain angle at which the string attached to the car is parallel to the ramp.
Apparatus set up for the experiment.
Experimental procedure: the experimental procedure for this lab was very straight forward, the first thing that we did in the lab was to measure the dimensions of the pulley using calibers, to then determine the moment of inertia of the pulley. After the measurements were made using the calibers we proceeded and calculating the moment of inertia of the pulley by adding all the moment of inertia of the pulley. After finding the moment of inertia for the pulley we did a video capture to determine the angular acceleration of the pulley, this was determined by doing a video analysis in which we determine the time it took to stop to then determine the total angle that it rotated, once we had the angular acceleration we proceed and calculated the rotational torque of the pulley, and after having these theoretical results we proceeded and run a trial to measure how long it would take the car to travel the ramp, once we measured the time we proceeded and calculate the time to then compare it to the experimental result.
Using the calibers to measure the dimensions of the pulley to then determine the moment of inertia of it
Measurement and calculation for the moment of inertia of the pulley
This calculation was made using the dimensions measured from the pulley
Calculation for the angular acceleration and frictional torque used the moment of inertia found in the previous calculation
Calculation for the time it takes the car to go down the incline using the values found in the revious calculations,
The results shown were the theoretical results , which are going to be compared to the actual results. The experimental result in this case found for the time was 8.97 seconds which is very close to the results found theoretically, which lets one infer that the experiment was carried out correctly following the correct assumptions and doing the correct calculations, the percent error for the experiment was very small due that it was less than one percent. The sources of error in this experiment can come from stopping the timer at the correct time, other might be a worong assumption made such as assuming that the string is parallel to the pulley
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