Why do objects with lower rotational inertia have more translational kinetic energy?

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Avah Leonard · Accepted Answer

Total kinetic energy of a rotating body is combination of translational and rotational kinetic energy  K  =      1    2    m      v    2    +      1    2    I      ω    2  Moment of inertia for most (simple) rigid objects can be generalized as   I  =  c  m      r    2  solid sphere has   c  =  2      /    5hollow sphere has   c  =  2      /    3solid cylinder has   c  =  1      /    2hollow cylinder has   c  =  1 etc.Total kinetic energy can then be written as  K  =      1    2    m      v    2    +      1    2    c  m  (  ω  r      )    2    =            1      +      c        2    m      v    2  From the work-energy theorem   Δ  K  =  W and if we assume that initial kinetic energy is zero, the final translational velocity is then  v  =            1              1        +        c                            2        W            m        =                    2        W                    m        +        I                  /                          r          2                    From this we can conclude that translational velocity v will be larger for smaller values of c, which also means smaller moment of inertia I.

Why do objects with lower rotational inertia have more translational kinetic energy?

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