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In the preceding chapter we observed that a particle would remain in equilibrium, in a state of rest, or in a state of uniform motion in a straight line when the resultant of all the forces acting on it was equal to zero. This condition for equilibrium was extended to larger bodies under either of two possible conditions: If the forces acting on the body were concurrent, that is, if they were directed toward a single point, the body could be treated as if it were a particle; or if the body moved with uniform translational motion in which every particle of the body moved in the same fixed direction with uniform speed, the whole body could be treated as though it were a particle. Many of the problems of the equilibrium of extended bodies do not fulfill these conditions. The forces acting on the body do not pass through a single point, and the motion of the body is not one of uniform translational motion but may include rotation as well. The motion of a body is often quite complicated, as in the case of a spiraling football. The ball is generally thrown so that it spins about its longer axis, but, in addition to its spinning motion, the axis of rotation itself rotates, and the ball has a general translational projectile-like motion superimposed upon the rotational motions.