How to Find the Instantaneous Axis of Rotation?

[iitjee10]

Homework Statement

A rod is placed between two smooth perpendicular walls such that each end of the rod touches a wall. The rod is released with the bottom end making an angle @ with the horizontal (ground). Using the concept of instantaneous axis of rotation find the following:
(a) The initial angular acceleration
(b) the path of the centre of mass
(c) The instantaneous acceleration of the center of mass

Homework Equations

The Attempt at a Solution

I attempted the question first without instantaneous axis of rotation and managed to solve it using Newton's Laws, torque equations and constraint relations (although i could not do the last part)

But this instantaneous axis of rotation I have never heard about. Can you please explain it to me what it is and its use here or in some simpler cases so that i can get the hang of it?

 

[kuruman]

If I understand the problem correctly, the rod's length is greater than the separation between the walls, so it has to make an angle θ with respect to the horizontal. Say the right end of the rod touches the wall at a higher point than the left end. Note that the rod can turn counterclockwise but not counterclockwise. When the rod is let go, instantaneously it rotates counterclockwise about its right end. That end is the instantaneous axis of rotation because any infinitesimally small time dt later, the axis of rotation is the center of mass.

 

[iitjee10]

oh no! consider the walls as that of a room one end of the rod is on the vertical wall while the other end is on the horizontal wall making angle @ with the horizontal. The question had a figure so I had to spend the time describing the figure