Core muscle groups are not directly utilized during a squat movement, now back yes and abs but to call that core muscles could be an overstatement.
Sorry bro, but after studying kineseology and biomechanics,, and being a personal trainer I am going to have to disagree with this statment. The core musculature is most definetly utilized during a squat.
The term "core" is often throw around and understood as having stron abdominal and back musculature. This can be misleading as the true defenittion of core stability should actually be refered to as the proper mangment of lumbo-pelvic rhythm. So with that defenition in mind lets take a look at the biomechanics of a squat (please don't take this as me trying to be a know it all or trying to talk down to you in any way. It is just that squats are often discussed and many times they are discussed improperly. That being said it does not mean that you have to agree with any of my statments

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When we squat our feet are typically about shoulder width apart and our toes are pointed slightly outwards. This can debated b/c some say toes should be pointed straight ahead however looking at the structure of the human body the femur does not approach the into the acetabulum at a 90degree angle. Rather, it approaches anteriorly to posteriorly which creates a natural foot potition of about 7 degrees of outward rotation of the foot.
Now looking at the muscles and how they can affect core stabalization (lumbo-pelvic rhythm). When we squat down we are going into hip flexion. The musculature which performs hip flexion is the illiacus, psoas major, rectus femoris, sartorius and TFL. When our hips go into flexion our biceps femoris, semimebrinosis, semitendonosis and gluteus maximus will pull on the pelvis. To much hip flexion and those muscle will cause us to go into a posterior pelvic tilt which is not safe (*this is not usually the problem when people do squats, it was just metioned for the purpose of discussing the musculature*). The same is true if our trunk/spine go into flexion ( the musculature of spinal flexion is the rectus abdominus, external and internal obliques bilaterally and the psoas major bilaterally), our Quadratus Laborum (back extensor muscle) will pull our pelvis into an anterior tilt, this is not safe either and is usually the place were most people run into problems during squats. If our spine goes into extension (arching our backs backward) then our trunk flexors (rectus abdominus, external and internal obliques bilaterally and the psoas major bilaterally) are going to pull our pelvis into a posterior tilt....not safe either. The hamsrings are a big problem when doing squats becuase usually they are tight in most people. This can be a problem becuase the hamstrings (biceps femoris, semitendonosis and semmebronosis) cross not only the hip but the knee. If your hams are tight you may have trouble getting down for a full range of motion squat. One way most people compensate for this is buy going into spinal flexion and causing an anterior tilt of the pelvis which is not good. Why? Becuase doing this is going to put a lot of strain on the erector spinae muscles which are not really going to be able to sustain the kind of load you are placing/compressing on your spine. Especially since they need to now pull your spine back up from flexion, placing the load out infront of your center of gravity, before you can perform the concentric motion of the squat, coming up......which conssts of knee extension. Also, of your soleus is tight you will have problem doing full ROM squats becuase they will inhibit your ability to dorisflex your foot enough to get down to 90 degrees.
So what is right???
Plave your hands on the top of your hips at your ASIS. Then squat down as far as you can without going into an anterior pelvic tilt. This is you range of motion for a squat for the time being because you want to strech your tght muscles so that you can eventually get down and do a full range of motion. The best way to think about it is like you are going to sit down in a chair. Often times I have clients stand out in front of a bench and tell them to just sit back onto the bench and when their butt touches go back up. Another analogy I use is when I tell them to think about having bags in their hands and they want to go through a door so the first thing they would do is put their butt back/out a little to open the door. Then I have them put their hands on their hips and I look for their range of motion and any anterior pelvic tilt. Another common thing debated is the whole "knees over toes" thing. In my opinion it is okay for your knees to come slightly over your toes as long as you are balanced and driving up though the arch of your foot. Why? Becuase keeping your knees behind your toes is not funcional IMO. When you walk are your knees behind your toes? When you go upo steps are your knees behind your toes? Set my point.
Sorry I got kind of off track and long winded but back to my point. The "core musculature" or the musculature that performs lumbo-pelvic rythm plays and enormus role in squats as it does on most every exercise we perform and everyday life.
Okay, anyone want to disagree or flame me on this????
Start..........NOW!!!!!
