to observe torque in rotational equilibrium?

Answer 1

The first answer has a couple of things wrong. First, torque is the product of force and the lever arm, not force and the distance the force acts through. Torque alone does not imply motion or energy. It must act through an angle to have an effect. Although it's true torque and energy have the same units, energy is force acting along the distance and is the scalar dot product of the force and distance vectors, whereas torque is force acting at right angles to the distance and is the vector cross product of force and distance. Second, bodies in orbit maintain a constant angular momentum, not rotation energy. If the system moment of inertia is I, angular momentum H = Iw where w is angular rate. Rotational energy E = Iw^2/2. Constant H does not imply constant E, since I can vary with the distance between the two bodies. Thus with constant H, if I is reduced by half, w must double. This means E doubles also.
I'm not sure exacty what the question asks for, but if a system is in rotational equilibrium I'd assume H is constant and therefore no torque is applied. Applying torque to the system would change H which could be observable as a change in w and/or I.

Answer 2

Torque is the product of a force and the distance that the force moves in rotation. It is measured in units of energy.(newton meters).
If two masses are to rotate together in an Orbit and maintain equilibrium ,their rotational Energy relative to their fulcrum(barry center)must be equal at all times.
The motion of the Earth and the Moon relative to each other is a good way to observe their relative motional energy.

It is very vely simple.