Ganesh is a champion in cricket in his school. When he is in the ground (for practice) and he used to whirl his bat in different style. His coach was Mr. Gunalan. The coach asked Ganesh to hold the bat at its handle and roatate fastly. But Ganesh could not do as his coach said, Ganesh developed pain in his hands. Then his coach told him to rotate the bat by holding it at its mid point. When Ganesh rotated at this position, he was able to rotate the bat faster. Ganesh was surprised and asked his coach how.
(i) What was coach's explanation to Ganesh ?
(ii) What is Radius of Gyration ? Give an example.
(iii) How moment of Inertia is related with Angular velocity ?

Explanation

(i) When any object of mass 'm' is rotated by holding at its edge, its mass due to rotation (i.e. Inertia due to turing effect) will be more. Due to this, if is not possible to rotate the bat with greater angular velocity. But by holding the bat at its centre and rotated, the Moment of Inertia easier will be less. So you can rotate it with a greater angular velocity `(omega)` Moment of Inertia is also called as Rotational Mass.
(ii) Radius of Gyration : Consider a table fan, which rotates through its Axis or rotation. G be the centre of gravity of the fan at a point some where below the axis of rotation. The perpendicular distance between the Axis of rotation and the centre of gravity of the object (fan) is called Radius of Gyration (K).
Example : Parctically it is used in air planes and other automobiles which need a balance but have irregular shape.
(iii) Relation between Moment of Inertia (I) and Angular velocity `(omega)`
`I prop (1)/(omega) , I omega =` a constant
i.e. Angular momentum L = I `omega`