In the preceding chapter we described the kinematics of a rigid body. In this chapter we study the dynamics of a rigid body that is rotating in an arbitrary manner about a fixed point. To make the analysis easier I will introduce tensors and dyads, physical quantities that may be new to you. (You may be using tensors for the rest of your life, so this is a good chance to learn them!) Once the necessary mathematical tools have been developed we will use them to obtain expressions for the energy and angular momentum of rotating bodies. Next we develop the equations of motion for rotating bodies; these are called Euler’s equations. Finally, we use these concepts to study two problems, a freely rotating body and a rotating body acted upon by a torque. As examples we consider the Earth and a spinning top. The Earth is approximately a torque-free spinning body and a top (or gyroscope) is an example of a spinning body subjected to an external torque.
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