{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CLASS4 - 1 CHAPTER 4 RIGID BODY ROTATION 4.1 Introduction...

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

View Full Document Right Arrow Icon
1 CHAPTER 4 RIGID BODY ROTATION 4.1 Introduction No real solid body is perfectly rigid. A rotating nonrigid body will be distorted by centrifugal force * or by interactions with other bodies. Nevertheless most people will allow that in practice some solids are fairly rigid, are rotating at only a modest speed, and any distortion is small compared with the overall size of the body. No excuses, therefore, are needed or offered for analysing to begin with the rotation of a rigid body. *I do not in this chapter delve deeply into whether there really is “such thing” as “centrifugal force”. Some would try to persuade us that there is no such thing. But is there “such thing” as a “gravitational force”? And is one any more or less “real” than the other? These are deep questions best left to the philosophers. In physics we use the concept of “force” – or indeed any other concept – according as to whether it enables us to supply a description of how physical bodies behave. Many of us would, I think, be challenged if we were faced with an examination question: “Explain, without using the term centrifugal force , why Earth bulges at its equator.” We have already discussed some aspects of solid body rotation in Chapter 2 on Moment of Inertia, and indeed the present Chapter 4 should not be plunged into without a good understanding of what is meant by “moment of inertia”. One of the things that we found was that, while the comfortable relation L = I ω which we are familiar with from elementary physics is adequate for problems in two dimensions, in three dimensions the relation becomes L = I ω , where I is the inertia tensor , whose properties were discussed at some length in Chapter 2. We also learned in Chapter 2 about the concepts of principal moments of inertia , and we introduced the notion that, unless a body is rotating about one of its principal axes, the equation L = I ω implies that the angular momentum and angular velocity vectors are not in the same direction. We shall discuss this in more detail in this chapter. A full treatment of the rotation of an asymmetric top (whose three principal moments of inertia are unequal and which has as its momental ellipsoid a triaxial ellipsoid) is very lengthy, since there are so many cases to consider. I shall restrict consideration of the motion of an asymmetric top to a qualitative argument that shows that rotation about the principal axis of greatest moment of inertia or about the axis of least moment of inertia is stable, whereas rotation about the intermediate axis is unstable. I shall treat in more detail the free rotation of a symmetric top (which has two equal principal moments of inertia) and we shall see how it is that the angular velocity vector precesses while the angular momentum vector (in the absence of external torques) remains fixed in magnitude and direction.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ 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