2017.01.02 Phys 2425 Notes Section 7 - Rotational Motion of Rigid Objects.pdf

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Rotational Motion of Extended, Rigid Objects I. Rotational Motion of Rigid Objects We want to extend our study of mechanics to extended, rigid objects. The word extended means that the object is made out of more than one particle, and the word rigid means that the particles always remain at fixed distances relative to each other as the object moves. The most common example of an extended, rigid object is a spinning wheel. The wheel is certainly composed of many particles, and the distances of those particles relative to each other do not change as the wheel spins. ( A rubber band, for example, would be an example of an extended, non-rigid object. It is certainly composed of many particles, but those particles do not remain at fixed distances from each other as the rubber band is stretched! We will not analyze such objects in this chapter .) In this chapter, we first define kinematic quantities for an extended, rigid object and then relate those quantities to the kinematic quantities from chapter 2, the quantities of the individual particles in the extended object. These kinematic quantities will very much mirror the kinematic quantities we defined in chapter 2 for individual particles. A. Angular Position The angular position of a particle is defined as the angle 𝜃 (in radians!!!!) that the particle makes from a reference line (usually chosen as the positive x- axis). See figure to the right.
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