Rotation of Rigid Bodies

Abstract

We have found that the motion of the center of mass of a multi-particle system can be determined from the external forces acting on the system. The general form of Newton’s second law allows us to find the motion from our knowledge of forces and force models for multi-particle systems, just as we have systematically done for particle systems previously. But what about the internal motion of the system or each part relative to the center of mass? Fortunately, in many cases we can simplify the system significantly by assuming that an object behaves as a rigid body: a body that does not deform. A solid sphere, a stiff rod, a ball with little deformation, or a molecule with little internal deformation, may in many cases be approximated as a rigid body without any internal deformation. This simplifies our description significantly: If the body does not deform, there are no internal energies associated with the deformation either: A rigid body can only be translated or rotated. In this chapter we will introduce the kinetic and potential energy of a rigid body. We find that it depends on the rotational inertia of a rigid body, called the moment of inertia. Rigid bodies with large moments of inertia require more energy to spin than rigid bodies with smaller moments of inertia. This gives us the tools we need to apply energy considerations to systems with rotating parts.