GME asked 1 year ago
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
Sazid Ahmad answered 1 year ago
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 and
for
.
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
.