Physics in Biology (Part II): Torque and Back Aches

(This is the 1st post in what I hope would be the start of a long series that would allow readers to appreciate the relevance of physics in biology, nursing, and other related fields.)

A lot of people suffer from back aches and you're probably even one of them. While most of us already know that it usually has something to do with posture, what few of us know is that it usually also has something to do with too much torque. i.e., wrong posture is just too much torque in the wrong places.

So first of all, what is torque?

Let me put it this way. There's a reason why doorknobs are placed opposite to the hinges - it is where we can apply maximum torque about the hinges.

Ah, so torque is dependent on the distances from the pivot points (the hinges in this case)? Yes. In most books it's called the moment arm. There are other factors that torque is dependent on. In our door example, we know that we can swing the door faster if we apply a large enough push on the position of the doorknob. We also know that the push is most efficient if we push perpendicular to the door.

Let us sum up what we have learned so far from the door example. Torque has something to do with three physical quantities:

1. the applied force - the amount of push we exert on the door;
2. the distance from the pivot (the hinges) to the point where the force acts; and
   
3. the angle between the force and the line that represents this distance
   

We can combine 2 and 3 to define a new term: the moment arm. i.e., the perpendicular distance of the force from the pivot point. Hence, maximum torque is obtained when we make the applied force and the moment arm as large as possible.

Ok. Enough of doors and lets get down to our business of back aches.

Imagine tilting your upper body forward. As you do that, there are two (2) main forces acting on your upper body. The first one is the weight of your body. You know it's there because it takes a lot of effort for you to stay in that position, and most of that effort goes to countering this force. The second one is the force of the back muscles that keep you from toppling over. Without this force, the weight force would easily rotate your body forward. By the way, when you're in this position, the pivot point is somewhere in the position of the hips.

Ah, so the weight of your upper body (let's call this Fw) produces a torque that strives to rotate your upper body forward. Simultaneously, the force of the back muscles (let's call this Fm) produces a torque that rotates your upper body backward. This is to keep your upper body in equilibrium, keeping you in that position.

To simplify our discussion, let us assume that the distances of both forces from the pivot are equal and we will call them L. Would this also mean that the two forces are therefore equal? Not quite. The more we bend forward, the angle between Fw and L increases. So, while Fw and L don't increase, the torque due to Fw (because of the increasing angle) does! Now, what about the back muscles? First of all, it is easy to imagine that the angle between Fm and L is quite small compared to the angle between Fw and L, and this doesn't change!... or at least not as much as the other angle. So if this angle and L doesn't change, then to keep your upper body in equilibrium, Fm has to increase. Now, since the angle between Fm and L is very small compared to the angle between Fw and L, we could just imagine that Fm should be very large compared to Fw in order to maintain equilibrium.

Let us now imagine that we are standing upright. When we do this, the angles that we have been talking about would now be zero. Hence, while Fw and Fm may still exist, the torque that they produce would now be zero.

(to be continued)