Tjcondit1



  


Q: given angular velocity, time and radius how to you figure distance
along the perimeter?

Answer:

To find a distance we need a rate (speed) multiplied by a time.

The tangential speed is given by the angular velocity times the radius 

 (1)      v = wr
 
      where w = angular velocity
      and   r = radius.      
       
The distance along a perimeter (of a circle) is the tangential speed times
time.  

 (2)    d = vt
     
     where d = the distance along the perimeter
           v = the tangential velocity defined in (1) above
           t = time
            
Substituting for v from (1) in the formula for distance (2) gives
              *************             
 (3)          *  d = wrt  *
              *************

Note: If the angular velocity is in degrees per second first multiply by
pi (3.14159...)
       and divide by 360 to convert w to radians per unit time.

Note: if w is not constant then the above is not true. We must replace wt
in formula (3)
      with an intrgral over time from 0 to t.
           /
      d = r| w dt
           /


Q: given the straight line velocity, time and radius how to you figure
distance along the perimeter?

Answer:
I will assume that you mean the tangential velocity when you say straight
line velocity.
In this case distance is just the straight line velocity times the time
and radius is
not needed! 

 d = vt
 
 Where d = distance 
       v = tangential velocity
       t = time.
       
If v is variable with time then you have to do an integral.         

           /
      d =  | v dt
           /

note: When text books speak of velocity they usualy mean a vector quantity
      but in the context of uniform circular motion they are usualy
talking
      about tangential speed.
      
note: I am a little suspicious about the wording of this question. I
wonder
      if what you really are asking about is angle?  If so the you can get
the
      angular velocity w by dividing v by r
      
           w = v/r
           
      the angle in radians swept out by an object moving along a circle
will be
      
           angle = wt
           
      where t is time. Substituting v/r for w in the above equation then
gives
      
          angle = (v/r)t