A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson.

  • Parkinson, Thomas, 1745-1830.
Date:
1785
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Licence: Public Domain Mark

Credit: A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson. Source: Wellcome Collection.

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    fiorn And if, as before, a plane be drawn through G, parallel to the axis, the fums of the moments of A, B> C, &c. multiplied into their perpendicular diftances, on each fide of this plane, are not equal, becaufe the velocities are not equal; and confequently if G be flopped, A, B, (7, &c. will not be quiefcent. But the late- ral efforts to move the plane paffing through S G perpendicularly to the axis, being fuppofed equal, it is evident that the center of percuffion will be in S G. 488. Prof. Let A, B, C, &c. be particles of a bodyy revolving 9 about an axis pafijing through the point S, it is required to find the center of percuffion. a* w Let Ay B, Cy &c. be the places of the particles reduced to th plane paffing through S G, perpendicular to the axis, by let- ting fall perpendiculars from them upon its and let A’s mo- ment or [A x SAy becaufe its velocity is as SA} be reprefented in quantity and direction by Ap perpendicular to SAy and re- folved into two forces Aq perpendicular, and pq parallel to SG. The whole moment of A: its force perpendicular to SG:: Ap {A n a\ a a a n / r* • i\ , A -A X S J~i. X S Cl x 8A) : Aq :: 8A: Sa (urn. triangles), and Aq= = A x Say and, fuppofing P to be the center of percuffion, the efficacy of A to communicate motion to P is equal tc its perpen- dicular moment multiplied into the diftance at which it afts = 8 A* Ax 8 a x Pm = Ax Sax S P — Sm = A x S a x SP S a Ax Sax SP— A x SA2. By a fimilar procefs it appears, that the efficacy of B, C, &c. to communicate motion to P, is B x S b X SP — B x SBzy C x SC2 —- C x S c x SP, &c.; and, becaufe P is quiefcent, thefe forces are equal on each fide of it, or Ax S a x SP — A x SA2 + B x S b x SP — B x SB2 = C x SC2 — C x Sc n T) J c CD AxSA2+BxSB'+CxSC2 x SPy and conlequently SP — A x S a -I- B x S b + C x S c &c. Q^E. I. 489. Con