Q.Explain balancing or mechanical equilibrium. Linear velocity of a rotating fan as a whole is generally zero. Is it in mechanical equilibrium? Justify your answer.

[!TLDR] Mechanical equilibrium means the net force on every part of a system is zero. Yes, a steadily rotating fan (as a whole) is in mechanical equilibrium, since its centre of mass stays fixed with zero net linear velocity/acceleration, even though individual blade points are moving in circles. [!ANSWER] Mechanical equilibrium = zero net force on every p …

MECHANICAL EQUILIBRIUM (or balancing) is the state in which the net (resultant) force acting on a body, or on every individual part of a system of bodies, is zero -- so that the velocity/linear momentum of every part remains constant (possibly zero), with no acceleration anywhere in the system (4.12).

A steadily ROTATING FAN, considered AS A WHOLE (i.e. its overall centre of mass, and its total/net linear momentum), does indeed have essentially zero net linear velocity and zero net linear acceleration -- the fan's centre of mass stays fixed in place (it is bolted to the ceiling/stand), so in this 'whole system' sense, the fan is correctly described as being in MECHANICAL equilibrium (translational equilibrium): the net EXTERNAL force on the fan is zero (its weight is balanced by the mounting support). HOWEVER, this does not mean the fan is entirely 'unmoving' or free of any acceleration everywhere: individual POINTS on the spinning blades are continuously moving in circles and hence continuously ACCELERATING (centripetal acceleration, always directed toward the rotation axis) even at constant rotational speed. So the fan is in TRANSLATIONAL/mechanical equilibrium as a system (net force zero, centre of mass motionless), while simultaneously NOT being in a state of zero acceleration for every individual pa …

Apply the definition of mechanical equilibrium (net force on the system/its centre of mass is zero) to the fan as a whole, distinguishing this from the (non-zero) …

Concluding the fan is NOT in equilibrium simply because its blades are visibly moving/accelerating, without distinguishing individual-particle acceleration from the net fo …