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 . 100 revolutions per minute is at the rate of 2tt X 100= (^-measure units) of angular space per minute= per second ; .\ ca = per minute or second. (2) A grindstone whose initial speed of rotation is 90 revo-lutions per minute is brought to rest in 30 seconds, the an-gular retardation (or negative angular acceleration) being con-stant ; required the angular acceleration, 6, and th
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 . 100 revolutions per minute is at the rate of 2tt X 100= (^-measure units) of angular space per minute= per second ; .\ ca = per minute or second. (2) A grindstone whose initial speed of rotation is 90 revo-lutions per minute is brought to rest in 30 seconds, the an-gular retardation (or negative angular acceleration) being con-stant ; required the angular acceleration, 6, and the angularspace a described. Use the second as unit of = 2tt|^ = per second; .*. from eq. (1) OD — QD 6 = —r-^ = — -=- 30 = — (^-measure units)t per square second. The angular space, from eq. (2) is a = Gjj + idf = 30 X - i()900 = (7r-measure units), , the stone has made revolutions in coming to rest and a point 2 ft. from the axis has described a distance s = ap == X 2 = ft. in its circular path. 111. Rotation. Preliminary Problem. Axis Fixed.—Forclearness in subsequent matter we now consider the following. DYNAMICS OF A RIGID BODY. 109 simple case. Fig. 124 shows a rigid body, consisting of adrum, an axle, a projecting arm, allof which are imponderable, and asingle material point, whose weightis G and mass M. An imponderableflexible cord, in which the tension iskept constant and = P, unwindsfrom the drum. The axle coincideswith the vertical axis Z, while the cord FlG. 124> is always parallel to Y. Initially (, when t = 0) M lies atrest in the plane ZY. Required its position at the end of anytime t (, at any instant) and also the reactions of the bearingsat 0 and Ox, supposing no vertical pressure to exist at Ox, andthat P and J^are at the same level. No friction. At any in-stant the eight unknowns, a, go, 6, X0, Y0, Z0, Xx, and Yx, maybe found from the six equations formed by putting 2X, etc
Size: 1738px × 1437px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
