## CHAPTER 14ROTATIONAL DYNAMICS FOR RIGID BODIES

If each element of a body be multiplied into the square of its distance from the axis OA and all these products be collected into one sum and if this is put = *Mkk*, which I call the moment of inertia of the body with respect to the axis OA, then the moment of force required to produce acceleration α will be *Mkk* · α.

· Leonhard Euler, in *Theoria Motus Corporum Solidorum seu Rigidorum* (1765)

### 14.1 ROTATION OF A RIGID BODY ABOUT A FIXED AXIS

The motion of bodies is determined by Newton’s laws. The detailed application of these laws, however, to actual problems such as the motion of the earth under all forces exerted on it by the sun, the moon, and the other planets is a complex matter. One of ...