Equilibrium

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Equilibrium

Consider these objects: (I) a book resting on a table. (2) a hockey puck sliding across a friction less surface with constant velocity. (3) the rotating blades of a ceiling fan. and (4) the wheel of a bicycle that is traveling along a straight path at constant speed. For each of these four objects:

1. The linear momentum P of its center of mass is constant.

2. Its angular momentum [ about its center of mass. or about any other point is also constant.

Our concern in this chapter is with situations in which the constant are in fact zero; that is. we are concerned largely with objects that are not moving in any way-either in translation or in rotation-in the reference frame from which we observe them. Such objects are in static equilibrium. Of the four objects mentioned  t the beginning of this section. only one-the book resting on the table is in static equilibrium.

The domino  is not quite as unstable. To topple this domino, a force would have to rotate it through and then beyond the balance position, in which the center of mass is above a supporting edge. A slight force will not topple this domino, but a vigorous flick of the finger against the domino  certainly will. (If we arrange a chain of such upright domino, a finger flick against the first can cause the whole chain to fall.).

(0) A domino balanced on one edge. with its center of mass vertically above that edge. The gravitational force F; on the domino is directed through the supporting edge. (b) If the domino is rotated even slightly from the balanced orientation. then F; causes a torque that increases the rotation. (c) A domino upright on a narrow side is somewhat more stable than the domino in (0). (d) A square block is even more stable

(0) A domino balanced on one
edge. with its center of mass vertically
above that edge. The gravitational force F; on the domino is directed through the
supporting edge. (b) If the domino is rotated
even slightly from the balanced
orientation. then F; causes a torque that
increases the rotation. (c) A domino upright
on a narrow side is somewhat more
stable than the domino in (0). (d) A
square block is even more stable(0) A domino balanced on one
edge. with its center of mass vertically
above that edge. The gravitational force F; on the domino is directed through the
supporting edge. (b) If the domino is rotated
even slightly from the balanced
orientation. then F; causes a torque 
increases the rotation. (c) A domino upright
on a narrow side is somewhat more
stable than the domino in (0). (d) A
square block is even more stable.

The child’s square block  is even more stable because its center of mass would have to be moved even farther to get it to pass above a supporting edge. A flick of the finger may not topple the block. (This is why you never see a chain of toppling square blocks.) The worker in Fig. 13-3 is like both the domino and the square block: Parallel to the beam, his stance is wide and he is stable: perpendicular to the beam, his stance is narrow and he is unstable (and at the mercy of a chance gust of wind).

The analysis oi static equilibrium is very important in engineering practice. The design engineer must isolate and identify all the external forces and torques that may act on a structure and, by good design and wise choice of materials, ensure that the structure will remain stable under these loads. Such analysis is necessary to ensure, for example, that bridges do not collapse under their traffic and wind loads, and that the landing gear of aircraft will survive the shock of rough landings.

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Equilibrium