Elementary Rigid Dynamics Volume 1

Elementary Rigid Dynamics Volume 1

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1891 edition. Excerpt: ...and is represented by the product of w into the perpendicular distance of A from OC'=m. OA sin GOA. But since the motion is also determined by the two given angular velocities about OA, OB, the motion of the point A is also represented by the product of OB into the perpendicular distance of A from OB = OB. OA sinBOA; sinBOA _ O0 Hence the angular velocity about OO is represented in magni tude by OO. From this proposition we may deduce as a corollary " the parallelogram of angular accelerations." For if OA, OB represent the additional angular velocities impressed on a body at any instant, it follows that the diagonal OO will represent the resultant additional angular velocity in direction and magnitude. 233. This proposition shows that angular velocities and angular accelerations may be compounded and resolved by the same rules and in the same way as if they were forces. Thus an angular velocity m about any given axis may be resolved into two, w cos a and w sin oz, about axes at right angles to each other and making angles a and 571'--oz with the given axis. If a body have angular velocities 10, m2, 0);, about three axes Ow, Oy, Oz at right angles, they are to_g_e@e_r_ ei1uvivalent to a single angular velocity w, where w = '/ml' ] (.022 + ma', about an axis making angles with the given axes whose cosines are respectively ii, is, This may be proved, as in the corresponding proposition in statics, by compounding the three angular velocities, taking them two at a time. It will however be needless to recapitulate the several propositions proved for forces in statics with special reference to angular velocities. We may use "the triangle of angular velocities" or the other rules for compounding...show more

Product details

  • Paperback | 156 pages
  • 189 x 246 x 8mm | 290g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236964071
  • 9781236964076