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Physics 211, Quiz 23

Question 1: Two wheels are the same shape and mass, but one is larger than the other:
      wheel A has mass   m = 2 kg,   radius  R(A) = 1 m
      wheel B has mass   m = 2 kg,   radius  R(B) = 2 m
Both wheels roll at the same angular speed: omega = 1.5 rad/s.

Which wheel has more rotational kinetic energy? Explain.

  Answer: The rotational kinetic energy depends on moment of inertia 
          and angular speed:

               rot KE  =  0.5 * I * (omega)^2

          The angular speed omega is the same for both wheels, but
          the moment of inertia is not.  The moment of inertia depends
          on mass and radius:

               I  =  (something) * (mass) * (radius)^2

          Therefore

               I(A)        (something) * (2 kg) * (1 m)^2         1
              ------  =   --------------------------------   =  -----
               I(B)        (something) * (2 kg) * (2 m)^2         4


          So  I(B) = 4 I(A).  That means that B has 4 times as much
          rotational KE as A.
          

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