CENTRIFUGES 79 



inward constantly to prevent the weight from taking its natural course, 

 that is, flying off at a tangent. This inward force, which accelerates the 

 mass toward the center of the circle, is centripetal force. Equal and oppo- 

 site to it is the outward centrifugal force. The centripetal force happens 

 to be easier to calculate. 



The magnitude of the force depends upon the speed of rotation and 

 upon the radius of the circle. If a wheel is turning with an angular 

 velocity of o) radians per second (a radian is the portion of the circum- 

 ference of a circle equal in length to the radius R), the velocity (v) 

 of a point on the surface is v = (oR. The velocity (in units of length 

 per unit of time) does not change, but because the point on the surface 

 of the circle is constandy changing direction, the point is subjected to 

 an acceleration oc = co-R. The centripetal force Fe is the mass (m) times 

 the acceleration, or Fc = m X w-R. The angular velocity (w) can be con- 

 verted to revolutions per second because lir radians is one full circle. The 

 centripetal force then becomes 



Fe = w(277-N)-R = m47r-N-R 



where N is revolutions per second. Centrifugal force is equal in mag- 

 nitude. 



The amount of force relative to gravity is a more useful figure than 

 this absolute Fr. Usually a relative centrifugal force (RCF) is calculated 

 by dividing by the force of gravity. The relative centrifugal force is ex- 

 pressed as "so many times g" or "so many g's." The force of gravity is mass 

 times the acceleration of gravity (980 cm/sec") so 



^^^ F. m47T-Nm 



KCr = -pr- = 



tg mg 



If we know R and can measure N, we can calculate the g's. Any new 

 centrifuge must be calibrated if we are to describe its performance 

 adequately. We measure N with a tachometer or stroboscope. These 

 instruments usually give revolutions per minute, so N = rpm/60. Fig- 

 ure 7-1 shows the results of the calibration of a centrifuge. 



Angle Heads: The heads or rotors in which the tubes are held at a 

 fixed angle develop a higher apparent centrifugal force than the swing- 

 ing bucket rotors. As shown in Fig. 7-2, particles moving downward 

 (away from the center) must move against the viscosity of the liquid in 

 which they are suspended. If the tube is inclined, the distance the par- 

 ticles must move against this counterforce is only the distance across the 

 tube instead of the full length. The particles in the angle head move 



