[<< wikibooks] Physics Course/Motion/Periodic Motion/Circular Motion
== Circular Motion ==

Circular Motion is a motion of an object along a circular path. If the speed of the body remains constant throughout the motion, the object is said to perform a uniform circular motion. 
For an object in uniform circular motion along a circular path of radius R and 
  
    
      
        
          
            
              r
              →
            
          
        
      
    
    {\displaystyle {\vec {r}}}
   be the position vector of the object with the center of the path as the and 
  
    
      
        
          
            
              r
              ^
            
          
        
      
    
    {\displaystyle {\hat {r}}}
   being the unit vector along it and T be the time taken to traverse the path once (period), the total linear distance covered in one period is (the circumference of the circle)

  
    
      
        s
        =
        2
        π
        R
      
    
    {\displaystyle s=2\pi R}
  The speed (or linear velocity) is then given by

  
    
      
        v
        =
        
          
            s
            T
          
        
        =
        
          
            
              2
              π
              R
            
            T
          
        
        =
        2
        π
        f
        R
        
        
        …
        
          (
          
            f
            =
            
              
                1
                T
              
            
            
            =
            
              
                frequency
              
            
          
          )
        
      
    
    {\displaystyle v={\frac {s}{T}}={\frac {2\pi R}{T}}=2\pi fR\qquad \qquad \ldots \left(f={\frac {1}{T}}\,={\textrm {frequency}}\right)}
  The linear velocity is a vector quantity whose direction at any given instance is tangential to the circle at that point.
The angular velocity around the circle is

  
    
      
        
          
            
              ω
              →
            
          
        
        =
        
          
            
              
                
                  
                    r
                    →
                  
                
              
              ×
              
                
                  
                    v
                    →
                  
                
              
            
            
              
                |
                
                  
                    
                      r
                      →
                    
                  
                
                |
              
              
                2
              
            
          
        
      
    
    {\displaystyle {\vec {\omega }}={\frac {{\vec {r}}\times {\vec {v}}}{\left|{\vec {r}}\right|^{2}}}}
  Due to the vector product, the angular velocity vector is perpendicular to the plane of motion.
With circle of radius R = 1

  
    
      
        ω
        =
        2
        π
        f
      
    
    {\displaystyle \omega =2\pi f}