Rearranging the relationship between torque, change in angular momentum, and time by dividing both sides by $\Delta t$ tells us that the net torque acting on an object is equal to the rate of change of its angular momentum:

In one dimension, on a graph where the vertical axis represents angular momentum $L$ and the horizontal axis represents time $t$, the term $\frac{\Delta L}{\Delta t}$ corresponds mathematically to the slope of the line. Therefore, the physical quantity of net torque is determined by finding the slope of the angular momentum-time graph.

To calculate the net torque during a time interval where the graph forms a straight line, one determines the slope of that linear segment. For a segment defined by an initial point $(t_i, L_i)$ and a final point $(t_f, L_f)$, the net torque is calculated as the change in angular momentum (rise) divided by the change in time (run):

If the graph is linear, the slope is constant, indicating that a constant net torque is acting on the object throughout that duration.

The sign of the slope tells you the direction of torque. A positive slope means torque increases angular momentum. A negative slope means torque decreases it. A horizontal line (zero slope) indicates zero net torque, so the system is in rotational equilibrium.