Controlling Force:
The resultant external force that controls the movement of the ball and behaves along the radial line towards the axis is known as controlling force. This force behaves at the centre of the ball. It is equivalent and acts opposite to the direction of centrifugal force.
The controlling force 'F' = m ω2 r.
Or
For controlling force diagram in which 'F' is plotted against radius 'r', F/ r shows slope of the curve.
That is
F/r = tan φ ∝ N 2 . . . (12.29)
Hence, for a constant governor slope in controlling force diagram must increase along enhance in speed.