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

This is College Physics Answers with Shaun Dychko. We are going to study the change in angular velocity when two people push a merry-go-round instead of one and with two people, we are getting twice as much torque and so how do we use the data that we collect? Well, we would... first piece of data is the number of people pushing so it's 1 or 2 and then the second piece of data is the change in angular velocity in each case and so the change in angular velocity is angular acceleration times the amount of time during which this torque is applied and we know that the total torque on the merry-go-round is its moment of inertia times angular acceleration which we can then rearrange for α by dividing both sides by I. So the angular acceleration is torque divided by moment of inertia and we can plug that in here and now we have change in angular velocity in terms of torque. So we are going to, you know, look at the merry-go-round and count the number of times that it rotates in a given amount of time and keep the time the same that makes our math a little bit simpler because Δt does not need a subscript in that case and we'll have the change in angular velocity in the first case will be the first amount of torque times Δt over I and the merry-go-round's moment of inertia is not changing so there's no need for a subscript on the moment of inertia factor here and in the second case, we have a new torque which is 2 times the original torque times the same time divided by the same moment of inertia. So we can verify that we get twice as much change in angular velocity by dividing these two and we'll have 2τ 1Δt over I divided by τ 1 times Δt over I, which is 2 and if we can verify that then we have confirmed that twice as much torque gives twice the change in angular velocity.