The 10-lb-uniform rod AB has a total length of 2L = 2 ft and is attached to collars of negligible mass that slide without friction along fixed rods. If rod AB is released from rest when θ = 30°, determine immediately after release (a) the angular acceleration of the rod, (b) the reaction at A.
Consider the acceleration of the rod AB about its center of gravity.
The acceleration of center of gravity G with respect to the point A is given by,
Here, r is the distance between point A and G.
Substitute L for r.
From the acceleration triangle, acceleration of G is given by,
Calculate the mass moment of inertia of the rod AB.
Here, m is the mass of the rod and l is the length of the rod.
Substitute for l.
Consider the rod AB as the system and model it as a rigid body.
The free body diagram and the mass acceleration diagram of the system are as shown.
Consider the moment of forces about point P.
Substitute for and for
Substitute for g, for L andfor.
Therefore, the angular acceleration of rod AB is.
Apply force balance in y – direction.
Substitute for g, for 1 ft for for W and for .
Therefore, the reaction at point A is.