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.

P16.118

Step: 1

Consider the acceleration of the rod AB about its center of gravity.

Step: 2

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,

Substitute for.

Step: 3

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.

Step: 4

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.

Step: 5

(a)

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.

(b)

Apply force balance in y – direction.

Substitute for.

Substitute for g, for 1 ft for for W and for .

Therefore, the reaction at point A is.