The assembly shown consists of a solid sphere of mass m=2 kg and the uniform sle

Question

The assembly shown consists of a solid sphere of mass m=2 kg and the uniform slender rod of the same mass, both of which are welded to the shaft, where dimension b is 0.5 m, dimension c is 0.4m, r = 0.2 m, and the angular beta is 30 degree. The assembly is rotating with angular velocity omega = 30 rad/s, which is increasing at the rate of 3 rad/s^2. Find the total dynamic loading of the shaft at the support at O. GIVEN: m_s = 2 kg m_b = 2kg b = 0.5 m C = 0.4 m Gamma = 0.2 m beta = 30 degree omega = 30 rad/s

Explanation / Answer

SOLUTION:-

Moment of inertia of sphere about its own axis = 2/5 mr2 = 2/5 x 2 x 0.22 = 0.032 kgm2

Moment of inertia of sphere about point O = mb2 = 2 x 0.52 = 0.5 kgm2

Moment of inertia of slender rod about its own axis = 1/12 mc2 (Sin30) = 1/12 x 2 x 0.42 x 0.5 = 0.013 kgm2

Moment of inertia of rod about point O = mb2 = 2 x 0.52 = 0.5 kgm2

So, total moment of inertia of the system (I) = 0.032 + 0.5 + 0.013 + 0.5 = 1.045 kgm2

By formula dynamic loading DL = I x = 1.045 x 3 = 3.135 Nm (ANSWER)

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