Question

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Fall 2018 EGN 3311 Statics P80 HW #16 Problem 10.97 The frustrum of the cone has a conical depression. The material has a density of 200 kg/m3 Suppose that a -06 m, b-09 m, and た0.15 m (Figure 1) Part A Determine the moment of inertia I, of the frustum of the cone Express your answer to three significant figures and include the appropriate units. Submit Figure 1 of 1 Provide Feedback 2r

Answer 1

a = 0.6: b = 0.9 r = 0.15 m p = 200 kg/m^3 I_2 = I_1 + I_2 + I_3 Complete solid I_1 = 3/10 m_1 r^2_1 m_1 = p_1 v_1 = p/3 pi r^2_1 h_1 I_1 = 3/10 times rho times 1/3 pi r^2_1 h_1 times r^2_1 = 1/10 times rho times pi r^4_1 times h_1 I_1 = 1/100 times 200 times pi times (0.3)^4 times 18 = 0.916 kg m^2 Negative strip I_2 = -1/10 rho pi r^4_2 h_2 = -1/10 times 200 times pi times (0.15)^4 times 0.9 I_2 = -0.02863 kg m^2 Negative depression I_2 = -1/10 rho pi r^4_3 h_3 = -1/10 times 200 times pi times (0.3)^4 times 0.6 I_3 = -0.3054 kg m^2 I = I_1 + I_2 + I_3 = 0.916 + (-0.02863) + (-0.3054) I_2 = 0.582 kg m^2