Load factor as a result of constant roll rate

[ENgez]

The fuel pressure load equation for an aircraft in a constant roll maneuver has the term (as a result of the roll maneuver):

$\frac{\dot{\phi^2}}{2g}R^2$

where

$R$ - radius from center of fuselage
$g$ - gravitational constant
$\dot{\phi}$ - roll rate

my question is where does the "2" next to the gravitational constant come from?

 

[Illmatic1]

The “2” next to the gravitational constant is related to the fact that the equation is derived from a centrifugal force equation and is used to account for the acceleration of the aircraft due to the roll maneuver. In this equation, the centrifugal force is equal to the mass times the square of the angular velocity, multiplied by the radius from the center of the fuselage, divided by two times the gravitational constant. The factor of two accounts for the acceleration of the aircraft as it rolls.