Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . ight form a couple, or Y1 and Y0similarly) 2 (moms.)zand 2 (moms.)F must each = zero. Thenecessary peculiar distribution of the bodys mass about theaxis of rotation, then, must be as follows (see the equations of§122): First, x and y each = 0, , the axis must he a gravity-axis. Secondly, fdMyz = 0, and fdMxz = 0, the origin being any-where on Z, the axis of rotation. An axis (Z) (of a body) fulfilling the
Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . ight form a couple, or Y1 and Y0similarly) 2 (moms.)zand 2 (moms.)F must each = zero. Thenecessary peculiar distribution of the bodys mass about theaxis of rotation, then, must be as follows (see the equations of§122): First, x and y each = 0, , the axis must he a gravity-axis. Secondly, fdMyz = 0, and fdMxz = 0, the origin being any-where on Z, the axis of rotation. An axis (Z) (of a body) fulfilling these conditions is calleda Free Axis, and since, if either one of the three Principal Axesfor the centre of gravity (see § 107) be made an axis of rotation(the other two being taken for X and Y), the conditionsx = 0, y = 0, fdMxz = 0, and fdMyz = 0, are all satisfied,.it follows that every rigid hody has at least three free axes-,which are the Principal Axes of Inertia of the centre ofgravity at right angles to each other. In the case of homogeneous hodies free axes can often bedetermined by inspection : , any diameter of a sphere; any 130 MECHANICS OF ENGINEERING. dM dP *>. Fig. 141. transverse diameter of a right circular cylinder through its centre of gravity, as well as its geometrical axis; the geomet-rical axis of any solid of revolution ; etc. 124. Rotation about an Axis which has a Motion of Translation.—Take only the particular case where the moving axis is agravity-axis. At any instant, let thevelocity and acceleration of the axis be vand p; the angular velocity and accelera-tion about that axis, oo and 6. Then, since-rP the actual motion of a dM in any dt iscompounded of its motion of rotationabout the gravity-axis and the motion oftranslation in common with that axis,we may, in forming the imaginary equiva-lent system in Fig. 141, consider each dM as subjected to thesimultaneous action of dP = dMp parallel to JT, of the tan-gential dT = dMOp, and of the nor
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
