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Alternate Forms of Moment Equation (example continued)

Apply:

Σ F = m a_C

Euler’s First Law

A_x i + ( Ay – W ) j = ma_Cx i + ma_Cy j

In scalar form: A_x = ma_Cx and Ay – W = ma_Cy

The unknowns are A_x , a_Cx , Ay , and a_Cy So there are 2 equations and 4 unknowns.

Need additional information from kinematics relating the acceleration of the center of mass.

a_C = a_A + a_C_/A= 0 - ω² r_AC + α k x r_AC where r_AC = L/2 cos θ i + L/2 sin θ j

a_C = - ω² [ (L/2) cos θ i + (L/2) sin θ j ] + (Lα/2) cos θ j - (Lα/2) sin θ i

a_cx = - (Lω²/2) cos θ - (Lα/2) sin θ

a_cy = - (Lω²/2) sin θ + (Lα/2) cos θ

Lα/2 = - (3/4) g cos θ and Lω²/2 = (3/2) [ 1 – sin θ ] put into a_cx and a_cy

a_cx = - (3/2) [ 1 – sin θ ] cos θ + (3/4) g cos θ sin θ

a_cy = - (3/2) [ 1 – sin θ ] sin θ - (3/4) g cos² θ