EXAMPLE 4: Euler's equations for 2-D motion

At the instant shown, the uniform bar of mass m and length l is released from rest. Calculate the acceleration of A, the reaction at A and the angular acceleration of the bar at this instant.

Solution:

Kinematics relation:

At the point of release from rest , so that

We can now substitute (4) and (5) into (1), (2) and (3) and solve for the three unknowns to get