Having trouble understanding General moment

[Parker Kary]

On the website http://www.real-world-physics-problems.com/physics-of-billiards.html

they take this equation ∑M_g = I_G∝ where ∝ = -a_gx/r for the rotation of a rigid body where there is no slipping

They then change the equation to F⋅(h-r) = I_G(-a_gx/r)

why is ∑M_G = F⋅(h-r) when ∝= -a_gx/r?

 

[Stephen Tashi]

If we have a lever CD pivoting at point C and with a force applied at D, one way to compute the torque of the force about the point C is multiply the component of the force that is perpendicular to CD times length CD. Another way is to imagine that CD is replaced by a lever that pivots at C and is perpendicular to the line of the force. Let this lever intersect the line of the force at point Y. The moment of the force about C is the length CY times the magnitude of the force. If you use the latter method the length of CY is h-r.