The centripetal acceleration is given by
Where m is the mass of object, v is the linear speed of object and r is the radius of the circle or length of string.
this means for F to increase we need larger mass, greater linear speed and shorter string.
A large string would results decrease in centripetal acceleration.
Increasing the angular speed of a rotating body will not cause an increase in Moment of inertia because it depends on mass of object and distance from rotation axis. It does not depend on angular speed.
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