Equilibrium of Rigid Bodies — Definition

Definition

Imagine an object that doesn't change its shape, no matter how much force you apply to it – that's what we call a 'rigid body' in physics. Think of a solid brick, a metal rod, or even a planet; for practical purposes, they don't deform.

Now, what does 'equilibrium' mean for such an object? In simple terms, it means the object is balanced and not accelerating. This balance needs to be considered in two ways: how the object moves from one place to another (translation) and how it spins or rotates (rotation).

For an object to be in translational equilibrium, all the forces pushing and pulling on it must cancel each other out. If you push a box from the left with a certain force and someone else pushes it from the right with an equal force, the box won't move.

The net force is zero. If it was already moving, it would continue moving at a constant speed in a straight line. So, the first condition for equilibrium is that the sum of all external forces acting on the rigid body must be zero ($Sigma \vec{F} = 0$).

But that's not enough for a rigid body. Imagine pushing a door near its hinges and then pushing it near its handle with the same force. The door will rotate much more easily when pushed near the handle.

This rotational effect of a force is called 'torque'. For a rigid body to be in rotational equilibrium, all the torques trying to make it spin in one direction must be perfectly balanced by torques trying to make it spin in the opposite direction.

If you have a see-saw, and two people of equal weight sit at equal distances from the center, it balances. The torque due to one person is cancelled by the torque due to the other. So, the second condition for equilibrium is that the sum of all external torques acting on the rigid body about any point must be zero ($Sigma \vec{\tau} = 0$).

When both these conditions are met simultaneously – no net force and no net torque – then the rigid body is said to be in complete equilibrium. If it was initially at rest, it stays at rest (static equilibrium). If it was initially moving with a constant velocity and rotating with a constant angular velocity, it continues to do so (dynamic equilibrium). For NEET, we primarily focus on static equilibrium problems, where the body is initially at rest and remains at rest.