EguATioxR OF Motion. 



oil 



Then A';«= impressed force in the direction of r;-^m = 



etfective force due to the acceleration in ii; the centrifut^al 

 force —rv^m (see note, p. 2) results from the velocity vj the 

 centrifugal force contributed by w is — r sinO w'-ni. (see note, 

 p. 2) in the direction of OD, and this gives the component 



fii) 



— r sin '^0 w'ln along the radius vector r; — dr rdo r sin d<f = 



(Ir 

 the difference in pressure on the two opposite faces. 



Equating and transposing as before 



A — = ry— r sm (> w . 



I'dr of 



With reference to the direction of (>, we have 

 Fm= impressed force, 



r — »i=effective force due to the acceleratic^u 



in angular velocity v. 



df} 

 f>-^^m= difference in pressure on the opposite faces. 

 rdo 



Since as a particle moves from E to F it is carried by ?t the 

 distance EE, it falls behind by an amount equal to dr do. 

 which, wdien expressed in terms of force, is equivalent to 



2 iiv (see note, p. 3). 



Multiplying by mass, 



2 nv m 



represents the component of etfective force contributed by 

 the combined action of ii and v; w cannot exert an etfective 

 force such as this, since the particle always moves in the same 

 parallel, but it does exert a centrifugal force in the direction 

 of 0^ or rather there is an effective component of the centri- 

 fugal force acting in the direction of due to w. We already 

 know (see above) that the centrifugal force due to ic along 

 OD is 



— r sin ir. 



Since the tangent to EF at E makes an angle (> with ()/K the 

 component of 



— r sin i> w^ 



