A treatise on the rectilinear motion and rotation of bodies; with a description of original experiments. Relative to the subject / By G. Atwood.

  • George Atwood
Date:
1784
Catalogue details

Licence: Public Domain Mark

Credit: A treatise on the rectilinear motion and rotation of bodies; with a description of original experiments. Relative to the subject / By G. Atwood. Source: Wellcome Collection.

    456/484 page 432
    Prop. V. Cor. z. t 432 ] F is evanefcent or inconfiderable. But becaufe the angular velocity of the ftriking body is M, and the velocity of its centre of gravity “ V, the velocity of L is = r+ 2MC x GL: the equivalent mafs will G X therefore be ■ ■ T~^ impinging with the velocity V+ 2MC x GL. This impaCt will generate in the centre of GL . , 6 1 IVxG^+GL* direction WH: wherefore after the impact the velocity of the centre of gravity W in the fame direction will be V— GxG^x/^+zMCxGL moreover, the fame force of IV x G^J; + GL2- impaCt will generate an angular velocity in the fyftem GQ x V+zMCxGL * Cor. 3. *JVTEF~ —-■ „—- ------—, which being 3 zCxfVxfVT'xG^+GL1 6 added to the angular velocity before the impaCt N or fub- traCted from it, according as the impaCt tends to augment or counteract the rotation of the body (truck, the angular velocity of the fyltem IVTEF will be obtained. Let A reprefent the angular velocity of the fyftem WTEF immediately after the impaCt which has been juft determined, then if C be — 3.14152, Sec. zCAxfVE will be the velocity of the point E, or of the point F in the ftriking body: for according to the reafoning contained ^Adfinem, in page 422*> when the furfaces at F are perfectly fmooth the point F of the ftriking body will proceed at the in- ftant after the impaCt in the direction FE, until the two bodies have a common velocity in the direction FE: in the line LE take LI equal to the fpace which would be de- feribed by the point E with the velocity 2CA x IVE in any ftandard particle of time. Let Y be the centre of fpontaneous rotation in the fyf- tem £)BGF: the motion of this point will not beaffeCled by the impaCt; its velocity and direction therefore will be the fame after the impaCt as it was before the fyftem fttDBGF impinged on the other body : becaufe the angular velocity of the ftriking body is M, in the direction from L to F, and the velocity of the centre of gravity V in the direc- tion GB, the velocity of the point Y before the impaCt will be V - zCM x GY or V- GL make YZ perpen-
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