A rigid body is made of three identical thin rods, each of length 'L' fastended together in the form of the letter 'H'. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of 'H'. The body is allowed to fall from rest from a position in which the plane of 'H' is horizontal. What is the angular speed of the body when the plane of 'H' is vertical ?

A rigid body is made of three identical thin rods, each of length 'L'

1.	A rigid body is made of three identical thin rods, each of length 'L' fastended together in the form of the letter 'H'. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of 'H'. The body is allowed to fall from rest from a position in which the plane of 'H' is horizontal. What is the angular speed of the body when the plane of 'H' is vertical ?
Answer» Solution :The MOMENT of inertia of the system about the axis is `I=(4)/(3)ML^(2)`. By conservation of mechanical energy the lose in PE of BODY is equal to the gain in rotational KE. `:.(3)/(2)MGL=(1)/(2)((4)/(3)mL^(2))omega^(2)` on solving `omega=(3)/(2)sqrt((g)/(L))`