What is Meant by Linear Rotational Static and Dynamic Equilibrium

Still waters are said to run deep. It is clear that something is causing it to stay still, since the more “normal” waters surrounding it are swaying and heaving in every manner. It may also be appreciated that the cause is not a trivial one. If told that there is an object in deep space that is perfectly still, one would think that perfectly natural. There was nothing in its surroundings to affect it, neither bodily impulse, gravity nor force fields. Therefore, according to Newton’s first law, a body at rest stays at rest.

However, in the hustle and bustle of normal surroundings, stillness draws attention. Statics is a field entirely devoted to investigating stillness of stationary objects, not in the trivial case of a body in deep space, but rather in the midst of various forces acting on it. All forms of construction are based on statics. A construction, in the end, needs to withstand all possible forces of disruption. Engineers and architects appreciate statics as one of the most useful part of their inventory.

If in the midst of various forces a body remains still, it is said to be in equilibrium. This only expresses the fact that all the forces are cancelling each other out. A force produces two kinds of changes in an object’s position – linear and rotational. Linear means that the object moves from one point to another, while rotational implies just that, i.e. a rotation of the body around whatever axis.

Of course both kinds of displacement may take place at the same time. Making the distinction between linear and rotational displacement allows us to study the two aspects separately. In other words, we may identify exactly which force causes the body to move, and which to rotate.

Consider a body suspended from two unequal lengths of string, each fixed at a different point above it. We know that there are three forces acting on the body – the weight of the body acting directly downwards, and the tensions in the two strings (T1 and T2), acting at certain angles to the vertical (θ1 and θ2), and whose magnitudes are unknown. The key to solving problems in statics is using the fact that there is no net force, for otherwise the body would be accelerating. Therefore, taking components of the forces in both the vertical and horizontal directions, gives two simultaneous equations involving T1 and T2, which may be solved.

If a body is fixed at a certain point, rotation is caused by a force applied at any other point on the body which doesn’t go through the fixed point. It can be described as a rotational force, and is called torque. Torque is a vector that is used generally in physics to describe dynamic situations, but is statics it acquires a more simpler form, called moment of force. A moment of force is computed simply by taking the force at right angles to the line connecting the point of application and the fixed hinge, and multiplying with the distance between two points. This is the moment of force “around” that point.

In a fixed construct, there is no movement, and therefore no rotation. In the parlance of physics, it is said to be in rotational equilibrium. The immediate consequence is that, the sum of all the moments around any point on it must be zero. This is a central tenet of statics, known as the principle of moments.

Equilibrium is further described in terms of being static and dynamic. This is merely a consequence of Newton’s first law, which states that, in absence of an applied force, a still body remains still, and one that is moving with constant velocity will continue in the same way. In statics, where net force is always zero, bodies are said to be stationary. But they very well may be described as having constant velocity, which neither adds nor takes away anything in terms of physics. Static equilibrium is merely a descriptive term for one, while dynamic equilibrium describes another. Therefore, the chair may be in static equilibrium on the harbor, while it is in dynamic room on the deck of a ship moving with constant velocity.

Actually, this distinction is made redundant through Einstein’s theory of special relativity. According to this theory, the word “stationary” makes no sense. All frames of calculation are relative to each other. If we take the frame to be moving with the ship, then it is the chair on the ship’s deck that is stationary, while that on the harbor is moving. In statics, the frame of the stationary body is always taken as reference, and therefore always concerns static equilibrium.