**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

_{}

_{}

_{}