MMAN2300 2014 Problems Solving Exercise #3

A uniform rigid rod of length L is positioned as shown so that it makes an

angle with the horizontal surface. There is no friction between the rod and

the surface. The rod is then released from rest.

(a) Draw a free body diagram of the rod. Label the point on the rod

that touches the surface as A

(b) Sum forces on the rod and conclude that the centre of mass has no

horizontal acceleration.

(c) Express the position of A with respect to G as a vector

(d) Use a cross product to find the moment about the centre of mass

(e) Perform a moment balance about the centre of mass (for a slender rod: = 1122)

(f) Show that you now have 2 equations for 3 unknowns

(g) Use rigid body kinematics to develop a vector equation that relates the accelerations of

point A and the centre of mass at this instant. You may assume that A does not leave the

surface.

(h) Show now that you have 4 equations for 4 unknowns.

(i) Use the equations you have developed to show that = cos

(16+12cos2 )

Suggested additional exercise (NOT for marks): Show that we can arrive at the same answer by

performing the moment balance about point A.