Why is it necessary for a body to have the net torque acting on it be balanced along with the forces for it to be in equilibrium? Isn't torque just some special case of force like rotation is a special case of translation? Why doesn't it suffice to have only the forces balanced for the body to be in equilibrium? I know there are examples which prove otherwise, but I need a more theoretical explanation. The case where the net torque is zero even when the force is not is understandable, since torque only represents the rotary component of force.
There would have been no need of introducing the concept of torque if we were only concerned with motion of a point particle (as the name suggests, it is hypothetical physical object having mass but no size). There is no concept of rotation of a particle and thus no need to introduce the concept of torque.
The concept of torque arises when we are concerned with system of particles. Here, there is a possibility that the net force on our system is zero but still the body is somehow moving. This possibility arises because the forces may act on different particles and there may exist internal interactions as well,causing the body to rotate if it is rigid.
That is how the introduction of the concept of torque is justified.
Torque is qualitatively a twisting force. Therefore, if net torque is zero, then the body cannot rotate. And if net force is zero the body will not translate. That is why for mechanical equilibrium, both the conditions must hold .
I hope I made myself clear.
You can consider rotation and translation as two completely separate things. When all forces balance out, there is no translational acceleration. When all torques balance out, there is no rotational or angular acceleration. And we need both to be 0 before saying that an object is in equilibrium.
When all forces balance out it just means that the object is not moving translationally but it can still rotate and spin on the spot.
Answer to the comments:
From your comment below:
if the net force on the point object becomes zero then so will the net torque
True so far that if two forces act on a point object and balance each other then their torques do also balance. Simply because they act at the same distance from the rotation point (reference point).
But for an object consisting of many points or particles, the forces do not necessarily act on the same points even though they balance out overall. We could have one force pulling up in a point on the right side and the same force pushing down in a point on the left side of the object. They cancel each other out when we look at the body as a whole. Think of the example with a bike wheel being spun that I gave in the comments.
So, this body as a whole does not translate. But the force locally at each of the points is not balanced. That point will translate locally. So they will cause torques that do not balance.
A torque is actually a manifestation of a force at a distance. By balancing the forces and the torques, you are matching the magnitude of force and the location where the force acts.
In simple terms, two equal and opposite forces acting on a body at rest will cause a rotation unless their line of action coincides. If they are offset from each other, then a net torque will be present and the body will rotate.
- Zero net force, assures the center of mass does not translate.
- Zero net torque about the center of mass, assures the body does not rotate.