Radial and Tangential Quantities

Radial and Tangential Quantities

Radians are worth using because they make it very simple to convert between angular and tangential quantities. If one uses degrees, one must constantly go back to "360 degrees equals one revolution, which is a distance two pi times the radius ..."

Given the angular velocity omega of an object, and its angular acceleration alpha, one can calculate

         tangential displacement     s  = R * omega * t

         tangential speed            v  = R * omega
                                      T

         tangential acceleration     a  = R * alpha

If an object moves along a circular path, but changes its speed as it moves (slowing down or speeding up), then it is NOT in uniform circular motion.

It retains a centripetal acceleration (towards center of circle) because, at any particular moment, it has some tangential velocity, and

                                            v^2 
         centripetal acceleration    a  =  -----
                                      c      R

But it also has a tangential acceleration due to its change in tangential speed; one way to express it is


         tangential accleration      a  =  R * alpha
                                      T

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