A milling cutter, mounted at the middle of an arbor, is used to remove metal from a workpiece (Fig. 4.78). A torque of \(500 \mathrm{~N}-\mathrm{m}\) is developed in the cutter under steady-state cutting conditions. One of the 16 teeth on the cutter breaks during the cutting operation. Determine the cross section of the arbor to limit the amplitude of angular displacement of the cutter to \(1^{\circ}\). Assume that the arbor can be modeled as a hollow steel shaft fixed at both ends.

Data: Length of arbor \(=0.5 \mathrm{~m}\), mass moment of inertia of the cutter \(=0.1 \mathrm{~N}-\mathrm{m}^{2}\), speed of cutter \(=1000 \mathrm{rpm}\).

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Overarm Arbor support Cutter Arbor- Column Table FIGURE 4.78 Cutter of milling machine. -Workpiece