Question
An electric screwdriver has two speeds, each of which exerts a different torque on a screw. Describe what calculations you could use to help you compare the angular momentum of a screw at each speed. What measurements would you need to make in order to calculate this?
Final Answer
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Solution video
OpenStax College Physics for AP® Courses, Chapter 10, Problem 24 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. We want to measure the angular momentum of a screw being rotated at the end of an electric screwdriver. So the electric screwdriver has two speeds so there's going to be two different angular momenta to calculate. The first thing we'll need to do is figure out the moment of inertia of the screw and we'll do that by measuring the diameter and the mass of the screw and then we'll calculate using this formula here which is from this picture here—figure [10.12]— and the screw was like a solid cylinder rotating about a cylindrical axis and that's going to be mass times radius squared over 2. Now measuring the diameter is easier than measuring the radius and so we plug in diameter divided by 2 in place of radius here. And so that's the moment of inertia and that's the first factor in this angular momentum formula and then we need to know the angular speed ω. So assuming that this screw is just rotating in space on the end of this electric screwdriver, it's not being driven into anything then we can look at it for 30 seconds say and count the number of revolutions that it does and we'll take that number of revolutions, divide by 30 seconds then multiply by 2π radians for every revolution and we are left with radians per second. And so we do that for the first speed and calculate the first angular momentum and then do that measurement of this speed again in the second speed setting of the electric screwdriver and get the second angular momentum.