Final answer:
A rotating fan can be in mechanical equilibrium if it rotates at a constant angular velocity with no net torque. While there may be linear velocity for parts of the fan, the fan is in dynamic equilibrium, not static, due to its motion.
Step-by-step explanation:
Mechanical equilibrium refers to a state where an object or system is not undergoing any acceleration, which implies that a net force of zero is acting upon it. However, this concept also applies to rotational motion. A system can be in rotational equilibrium if it is rotating at a constant angular velocity and there is no net torque acting on the system, resulting in no angular acceleration.
When considering the linear velocity of a rotating fan, the linear velocity of any point on the fan, except at the pivot, is not zero. Despite this, the fan can still be considered to be in mechanical equilibrium if it is rotating with constant angular velocity and not experiencing any unbalanced forces or torques.
Therefore, we say that the fan is in dynamic equilibrium. This is because it has a constant rotational motion without changes in its rate of rotation, fulfilling one of the conditions for mechanical equilibrium.
Therefore, the correct answer to whether a rotating fan with generally zero linear velocity as a whole is in mechanical equilibrium is (b) No, because the fan is rotating.
This choice recognizes that a state of rotational motion does not necessarily mean the system is out of equilibrium, but it must be emphasized that the fan is not stationary, hence not in static equilibrium. The actual motion of the blades means that they are not in a state of no motion—even though their linear path over time averages to zero at any point on the blade.