OpenStax College Physics for AP® Courses, Chapter 10, Problem 26 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. We are going to examine the difference in torques provided by two different speed settings on a table-top fan. So torque is moment of inertia times angular acceleration so the first step will be to figure out what is this moment of inertia and we'll measure the fan blade diameter and mass to calculate it and we use this formula that the moment of inertia will be the mass times radius squared divided by 2 for a disc rotating about a central cylindrical axis and I substitute in diameter divided by 2 in place of radius here and we square that multiply by mass and divide by 2 and that gives us I, the moment of inertia. Then we need to know the angular acceleration so that is the change in angular velocity over time and so let's suppose after 5 seconds say we measure the final angular speed which we'll have to take some time to measure itself maybe a further 2 seconds can be used to measure what this final angular speed is and we'll count the number of revolutions that happened during that 2 seconds and then divide that N by 2 and then multiply by 2π radians for every revolution and we get an answer in radians per second for our final angular speed and then the angular acceleration then is the final angular speed minus the initial, which was zero divided by the total time, which is 7 seconds—5 plus 2— and then we would have 1 torque would be the moment of inertia times the first angular acceleration on the first speed setting and then the second torque would be the same for the second speed setting.