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Physics 211, Quiz 19

Question 1: A space station rotates with uniform circular motion, at angular speed omega = 0.1 rad/s. For a point on the outer rim of the station, which is greater in magnitude: 
        A. centripetal acceleration
        B. tangential acceleration
        C. neither -- they are the same

  Answer: The centripetal acceleration of an object in uniform circular
          motion is

                                     (tangential velocity)^2
                  a(centripetal)  =  -----------------------
                                            radius


          The tangential speed at any point is  

                       v(T)       =  R * omega

          so it is greater than zero at any radius greater than zero.
          That means that the centripetal accleration is also greater
          than zero at any non-zero radius.

          The tangential acceleration is the change in tangential 
          speed.  But the station rotates with constant angular
          velocity, so that tangential speed is constant.  Therefore,
          the tangential acceleration is zero.

          So 
                         centripetal acceleration > 0
              
                         tangential acceleration  = 0

               --> centripetal acceleration is greater

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.