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Example using Mass Center Moment Form (continued)

Ex. 1 (continued)

Next apply Euler’s second law about the mass center, C.

Σ M_C = I_zz^C α

( - FR) k = I_zz^C αk

Calculate the moment of inertia of the entire wheel about its mass center, C. The wheel consists of three parts – the rim of radius, R, the eight spokes, and the hub. Calculate the mass moment of inertia of each part about its own center of mass and use the parallel axis theorem to transfer to the mass center of the entire wheel.

For the rim: I_zz^C= m_rim R² = (3/32.2) (2²) slug ft²

For the spokes: I_zz^C= 8 (1/12)m_spokes L_spoke² + m_spokes D_spoke²

L_spoke = R - r_o = 2 – (3/12) = 7/4 ft and D_spoke = 7/8 + ¼ = 9/8 ft

I_zz^C= 8 [ (1/12) (1/32.2) (7/4)² + (1/32.2) (9/8)² ] slug ft²

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