Net torque
Also called Sum of torques, Resultant torque
The signed sum of every torque exerted on a rigid system about one chosen axis. It equals the system's rotational inertia times its angular acceleration, and it is the slope of a graph of the system's angular momentum against time.
Add the torques, keeping their signs, about a single axis. That sum is what the rotational laws talk about, and none of them is about an individual torque.
The AP Physics 1 and AP Physics 2 sheets print the second law in rotational form as
and EK 5.6.A.2 states it in words: the rate at which the angular velocity of a rigid system changes is directly proportional to the net torque exerted on it and is in the same direction, while the angular acceleration is inversely proportional to the rotational inertia.
Signs, not vectors. The Topic 5.3 boundary statement puts the direction of torque beyond the scope of AP Physics 1, so the sum is one-dimensional: pick counterclockwise positive, or clockwise, then hold it. Two torques of equal magnitude and opposite sense cancel to zero.
One axis for the whole sum. Every term has to be taken about the same axis of rotation or the total is meaningless. Choosing that axis through a point where an unknown force acts is the standard move, because a force whose line of action passes through the axis contributes exactly zero.
A large force can contribute nothing. Torque needs a lever arm. Push straight at the hinge and the net torque is unchanged no matter how hard you push.
Zero is the interesting case. EK 5.5.A.1.iii gives the rotational analog of Newton's first law: a system will have a constant angular velocity only if the net torque exerted on it is zero. That condition has its own name, rotational equilibrium.
Read from a graph. EK 6.3.C.3: the net torque exerted on an object equals the slope of a graph of that object's angular momentum against time.
The balancing procedure itself lives in how to calculate torque.