Problem Graphic

Problem Diagram

The Principle of Work and Energy for a rotating body can be applied to this problem using

     T₁ + ΣU_1-2 = T₂

The applied work for a constant moment is

     U = M θ = (100 N-m) (4.459 rad)

        = 445.9 N-m

Now the input energy is known, the change in kinetic energy needs to be determined,

     T_start = T₁ = 0

     T_finish = T₂ = 1/2 m v_G² + 1/2 I_G ω²

              = 0 + 0.5 I_G (1.784 rad/s)²

             = (1.591 /s²) I_G

Equating the work done to the change in kinetic energy gives

     0 + 445.9 N-m = (1.591 /s²) I_G

Solving for I_G gives

     I_G = I_z = 280.3 kg-m²