Rigid body free essay sample

Conditions for Rigid-Body Equilibrium The rigid body in fgure (a), which is fixed in the x, y, z, reference at constant velocity. A free-body diagram of the arbitrary lth particle of the body is shown in fgure (b). There are two types of forces which act on it. The resultant internal forces, f , is caused by interaction with adjacent particles. The resultant external forces F represents, for example, the effects of gravitational, electrical, magnetic, or contact orces between the lth particles is in equilibrium, then appliying not included within the body. If the particle is in equilibrium, then applying Newtons first law we have When the equation of equilibrium is applied to each of the other particles of the body, similar equations will result. If all these equations are added together vectorially, we obtain The summation of the internal forces will equal zero since the internal forces between particles within the body will occur in equal but opposite collinear pairs, Newtons third law. We will write a custom essay sample on Rigid body or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Consequently, only the sum of the external forces will remain; and therefore, letting iF = if, the above equation can be written as Let consider the moments of the forces acting on the lth particles about the arbitrary point O, fgure (b). sing the above particles equilibrium equation and the distributive law of the vector cross product we have Similar equations can be written for the other particles of the body, and adding them together vectorially , we obtain The second term is zero since , as started above, the internal forces occur in equal ut opposite collinear pairs, and therefore the resultant moment of each pairs of forces about point O is zero. Hence , using the notation iMo = ir x iF , we have Hence the two equations ot equilibrium tor a rigid body can follows: be summarized as These equations require that a rigid body will remain in equilibrium provided the sum of all external external forces acting on the body is equal to zero and the sum moments of external forces about a point is equal to zero. The fact that these conditions are necessary for equilibrium has now been proven. They are also sufficient for maintaining equilibrium.