OpenStax College Physics for AP® Courses, Chapter 10, Problem 12 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. In this question, we study the change in angular momentum of a bicycle wheel when a force is applied to it. So change in angular momentum is moment of inertia times change in angular velocity and change in angular velocity is angular acceleration multiplied by time and we know that net torque is moment of inertia times angular acceleration and we can solve for α by dividing both sides by I and then we have this expression here which we then substitute in for α in our Δω formula and then replace this net torque because since there's only one force, it's gonna be that force multiplied by the distance from the center of the bicycle wheel to the force multiplied by sin of the angle between this lever arm and the force and all this can be substituted into our equation for change in angular momentum and we have finally an expression for angular momentum and this will help us decide which of the following measurements would be least helpful. So we can see that change in angular momentum depends on the force, the distance to the center of the wheel, the direction of the force and time. So part (a) is important because the more time that the force is applied, the greater the change in angular momentum. The radius at which the force is applied matters because it's directly proportional to that radius. The direction of the force is important because that's contained in this Θ here this angle because if the force were instead like this suppose then the angle between the force and the radius would be 180 degrees and the sin of 180 is 0 and there would be no change in angular momentum at all so the direction's important and so the answer to this question is (c), this is not important the angular velocity of the wheel when the force just began being applied.