Torque before slipping in a refrigerator

[mancity]

Homework Statement

A delivery truck is carrying a 120-kg refrigerator. The refrigerator is 2.20 m tall and 85.0 cm wide. The refrigerator is facing sideways and is prevented from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over? Assume that the center of gravity of the refrigerator is located at its geometrical center.

Relevant Equations

Torque=Fr

The solution lists out mg(b/2)=ma(h/2) and then proceeds to solve for a.
I am a bit stuck on how the initial equation is listed - why is the (b/2) swapped with the (h/2)? (namely, why isn't the equation mg(h/2)=ma(b/2)? My logic for this is y-direction and x-direction )
I feel that I am missing a fundamental concept here

 

[Orodruin]

Because the moment arm of the gravitational force relative to the tipping point is b/2 and not h/2.

It is a question about the met torque relative to the tipping point. Torque is the force multiplied by the distance between its line of action and the reference point.

 

[kuruman]

. . . why isn't the equation mg(h/2)=ma(b/2)? I feel that I am missing a fundamental concept here

You are missing a very fundamental concept. The lever arm h/2 is vertical and the force of gravity mg is also vertical. Since they are parallel, the torque is zero. The same applies to b/2 and ma except that they are parallel in the horizontal direction. The fundamental concept is that the cross product between two parallel vectors is always zero.

 

[Lnewqban]

...
I feel that I am missing a fundamental concept here