A rigid rod of length 2 L is acted upon by some forces. All...

A rigid rod of length $2 L$ is acted upon by some forces. All forces labelled $F$ have the same magnitude. Which cases have a non-zero net torque acting on the rod about its centre?
(a) 1 and II only
(b) II and III only
(c) I and III only
(d) The net torque is zero in all cases.
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Key Concepts

Torque

Torque is the measure of the tendency of a force to cause an object to rotate about an axis, pivot, or fulcrum. It is calculated as the product of the applied force and the perpendicular distance from the force's line of action to the axis of rotation. The direction of the torque is determined by the right-hand rule, and it plays a central role in analyzing rotational dynamics.

Net Torque

Net torque is the vector sum of all individual torques acting on a body. It determines the overall rotational effect on the object, and if the net torque is non-zero, the object will experience angular acceleration. Conversely, if the net torque is zero, the object is in rotational equilibrium, meaning it will not begin to rotate or will continue to rotate at a constant rate.

Moment Arm

The moment arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a key factor in calculating torque, as it defines the leverage that the force has. Even if forces are equal in magnitude, differences in the moment arms can lead to different torques, influencing whether the net torque on a system is zero or not.

Rotational Equilibrium

Rotational equilibrium occurs when the net torque acting on an object is zero, resulting in no change in the object's rotational state. This concept is crucial in statics and dynamics, as it helps predict whether an object will begin rotating or remain at rest when subjected to multiple forces.

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