Question

At the instant shown collar B moves with a velocity of vB=4 [m/s] and acceleration aB=2.4 [m/s2 ] to the right. Angle =50o , and length of the rod is L=650 [mm]. At the instant when =30o , determine (a) magnitude of angular acceleration of rod AB, AB [rad/s2 ], and (b) magnitude of acceleration of collar A, aA [m/s2 ].

What is magnitude of angular acceleration of rod AB, AB [rad/s2 ]?

What is magnitude of acceleration of collar A, aA [m/s2 ]?

Answer 1

Velocity of collars, v_B = 4m/sec Acceleration of collar a_B = 2.4 m/sec^2 theta = 30 degree, beta = 50 degree, L = 650mm Vector AB = L (cos theta i - sin theta j) AB = 0.65 times (cos 30 i - sin 30 j) = 0.65 times (0.86 i - 0.5 j) AB = 0.562 i - 0.325 j Velocity of collar VA = (cos beta i - sin beta j) = VA = (0.64 o - 0.76 j) V_A V_B = V_A + W_AB times AB Y_i = VA (0.64 i - 0.7 w) + wk (0.562 i - 0.325 j) Y_i = (VA times 0.64 + 0.32 w) i - (VA times 0.766 - 0.562 w) j comparing we get 0.642 VA + 0.325 W = 4 ____ (1) 0.766 VA + - 0.562 w = 0____ (2) VA = -3.68 m/s w = -5.02 m rad/sAcceleration of collar, a_B a_B = a_n - w^2