A uniform rod 0A of length l, resting on smooth surface is slightly disturbed from its vertical position. P is a point on the rod whose locus is a circle during the subsequent motion of the rod. Then the distance OP is equal to.. ?

Question

anonymous · Answer

attachment

vincent-lyon.fr · Answer

OP = l/4 ?

anonymous · Answer

dats ryt.. how did u get the answer?

vincent-lyon.fr · Answer

Well, I have no easy answer and what I did is not good enough to be posted here. There was some trial and error in it ;-) Mainly, I used these properties or facts: - in a rigid body, velocities obey a "twist" law; see: http://en.wikipedia.org/wiki/File:Velocity_twist.jpg - if table is frictionless, then reaction in A (bottom of rod) is vertical; so is weight. This proves that there is no net horizontal acceleration. The consequence is that velocity of centre of mass G is vertical. - velocity of A is horizontal. - displacement of A can be expressed wrt angle θ between vertical and rod and to length of rod ℓ. - using 'twist law' allows to express velocity of any point P on the rod with position αℓ from A. - velocity of P gets simple with components proportional to sinθ and cosθ if α = ¼ I cannot derive the whole thing using LaTeX in this window but I can write it down on paper and send a scan if needed.

anonymous · Answer

but then u havent applied the information that the point p is a locus of a circle and moreover what is the explanation of taking alpha = 1/4 ??