Condition of equilibrium for coplanar forces, one point fixed Condition of equilibrium for any forces, two points fixed Cases of forces which do no work Converse of principle for single particle Converse of principle for rigid body. Work done during initial motion necessarily positive Positions of stability and instability STATICS. CHAPTER I. STATICS OF A SINGLE PARTICLE. 1. WHEN a point is changing its position relatively to surrounding points, it is said to be in motion relatively to them if it is not changing its position, it is said to be at rest. If we consider not only the actual change of position, but also the time which the motion occupies, we bring in the idea of rate of motion or velocity. 2. Def. If a point moves over equal distances, in equal successive intervals of time, no matter how short the intervals are, the velocity of the point is said to be uniform. If the distances are not equal, the velocity is varying. For the velocity to be uniform, it is essential that the distances be equal, even when the intervals of time are indefinitely small: for instance, we may imagine a train travelling 30 miles during each of several successive hours, yet we should not describe its motion as uniform, if the distances travelled during the different minutes were not all equal, nor yet, even though the distances travelled during the different minutes were so, provided those travelled during the different seconds were not always the same, and so on indefinitely. |