(i) Consider an infinitesimally thin triangular strip having mass M and length L. Find the moment of inertia of the strip about on axis passing through its tip and perpendicular to the plane. Compare the result with moment of inertia of a uniform disc of mass M and radius L about an axis passing through its centre and perpendicular to the plane the disc. Why the two expressions are same?

(ii) A circular fan made of paper is in shape of a disc of radius R. The fan can be folded (various stages shown in figure `(a)` through `(f))` to the shape of a thin stick. The moment of inertia of the circular fan about an axis passing through centre O and perpendicular to the plane of the figure is `I_(0) = (1)/(2) MR^(2)` where `M =` mass of the fan.


(a) How does the moment of inertia (I), about an axis perpendicular to the plane of the figure passing through O, change as the fan is folded through stage a to b to c to d to e?
(b) When the fan is completely folded in the shape of a stick (fig. `(f))`, write its moment of inertia about the above mentioned axis.
Note : Moment of inertia of a uniform rod about an axis through its end and perpendicular to it is `(ML^(2))/(3)`

Answer

(i) `(ML^(2))/(2)`
(ii) (a) MOI does not change
(b) `I = I_(0) = (1)/(2) MR^(2)`