Question

A uniform slender bar AB of mass m has two light pegs A and B which are constrained to move in the frictionless circular slot with center O in the vertical plane. At the position depicted, the bar is released from rest. Find the bar's initial angular acceleration when the bar is released in terms of appropriate given quantities. The pegs each contact only one side of the slot at a given time.

Answer 1

Absolute acceleration of A with respect to the center of gravity G of the system a^vector_A = a^vector_G + a^vector_AG = a^vector_G + (alpha^vector times r_AG) a_A i = (a_xi + a_yj) + { (alpha k) times (- 1/2 sin 30 degree i + 1/2 cos 30 degree j)} a_Ai = (a_xi + a_yj) + (- 1/2 alpha sin 30 degree i + 1/2 alpha cos 30 degree j) Equate the coefficients of both sides 0 = a_y - 1/2 alpha sin 30 degree a_y = 0..25 alpha l Absolute acceleration of B with respect to the center of gravity G of the system a^vector_B = a^vector_G + a^vector_BG = a^vector_G + (alpha^vector times r_BG) a_B(sin 30 degree i + cos 30 degree j) = (a_xi + a_y j) + (- 1/2 alpha sin 30 degree j + l/2 alpha cos 30 degree i) Equate the coefficients of i on both sides a_B sin 30 degree = a_x + l/2 alpha cos 30 degree Equate the coefficients of j on both sides a_B cos 30 degree = a_y + l/2 alpha sin 30 degree Divide these 2 equations tan 30 degree