A block of mass m = 1.3 kg is suspended above the ground at a height h = 2.1 m b

Question

A block of mass m = 1.3 kg is suspended above the ground at a height h = 2.1 m by a spool with two arms. The spool-with- arms arrangement is a combination of a solid uniform cylinder of mass M = 4.0 kg and radius R = 0.4 m, and two rods, each of length I = 0.9 m and mass m_rod = 2.4 kg. What is in kg m^2 the moment of inertia of one of the arms around the rotation axis which passes through its center of mass (as shown)? What is in kg m^2 the moment of inertia of the solid uniform cylinder around the same rotation axis? What is in kg m^2 the moment of inertia of the whole spool- with-arms arrangement around the same axis?

Explanation / Answer

A) moment of intertia of rod = M*L2/12 = 2.4*0.9*0.9/12 = 0.162 Kgm2 Answer

B) Moment of intertia of solid cylinder = M*R2/2 = 4*0.4*0.4/2 = 0.32 Kgm2 Answer

C) Moment of interia of whole system = sum of individual moment of interia

= 2*moment_of_interia_rod + moment_of_intertia_cylinder = 2*0.162 + 0.32 = 0.644 Kgm2 Answer

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