Bodies affeSled by Fridlion. 
city generated by friction will alfo be the fame, to which if we 
add the velocity about the center at the beginning of the mo- 
tion, we {hall have the whole rotatory motion; hence there- 
r a ~ 7 —-^ — - — « — — .. 
fore, ‘U + — x £ — — 2F% = — 2F%, confequently %zz 
the fpace described before the motion be- 
comes uniform. 
2. If this value of ■% be fubftityted into the exp reffion for the 
Velocity, we fhall Ave for the velocity when the 
friction ceafes. 
3. I£.v=a, then z=o ? and hence -the body will continue to 
move uniformly with the firft velocity. 
4. If-'v be greater than a, then the rotatory motion of the 
point a on the plane being greater than its progreffive motion 
and in a contrary direction, the abfoiute motion of the point 
& upon the plane will be in the direftion ML, and confequently 
fri&ion will now ad in the dire&ion LM in which the body 
moves, and . therefore will accelerate the progreffive and retard 
the rotatory motion ; hence it appears, that the progreffive mo - 
ilonof a body may be accelerated by fridlion. Now to deter- 
mine the fpace defcribed before the motion becomes uniform, we 
may obferve, that as the progreflive motion of the body is now 
accelerated, the velocity after it has defcribed any fpace % will 
be ~ s/a + 2Fz, hence the velocity acquired = s/lFf zFz a 9 
and confequently the rotatory velocity deftroyed — x 
t/f + zF %-a r . hence v~ — x v/V + 2F2; Fz 9 
|fae§efore X = " * ” ' + x ' • the fpace required. 
