workshop 4 problem 1 - -1 Problem Moment of inertia The...

Info icon This preview shows pages 1–2. Sign up to view the full content.

1 Problem. Moment of inertia The purpose of this project is to calculate the angular momentum of the Earth. We will model the Earth as a solid uniform sphere with a mass density of ρ = 5500 kg / m 3 that rotates about its north–south axis once per day. The average radius of the Earth is a = 6378 km . The angular momentum of a rotating object is where I is the moment of inertia about the rotation axis and ω is the angular frequency in rad / s . Computing ω is straightforward and involves no calculus. The moment of inertia is computed relative to the axis of rotation: it measures how difficult it is to change the angular frequency of the object. The moment of inertia of a hollow cylinder, having mass M and radius r , and rotating about its axis of symmetry, is Mr 2 . (We assume the cylinder is empty, with no top or bottom, and with its thickness very small relative to r .) If an object lies within a distance R from the axis, and the differential dM describes the distribution of the object’s mass with respect to distance from the axis, then the moment of inertia (of the object about the axis, to be precise about what we’re measuring) is I = R 0 r 2 dM.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '07
  • BERMAN
  • Angular Momentum, Rotation, 5 rad, 106 m, 3 15 g, 8 5500 kg

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern