Understanding the scalar formulation of the moment of a force and applying it correctly through problem-solving is crucial in designing and analyzing mechanical systems. Here are the steps for problem-solving with the moment of a force:

1. Draw a free-body diagram (FBD) of the system. The FBD is a basic problem-solving step. It is a diagrammatic representation of all the forces acting on the system. Every force acting on the system must be identified and included in the FBD.
2. Identify the axis or point about which the moment is calculated. In some cases, the axis or point about which the net moment needs to be calculated is provided. However, in other cases, the problem requires selecting an appropriate axis or point.
3. Calculate the perpendicular distance between the force and the axis or point. The perpendicular distance is the shortest distance between the force and the chosen axis or point.
4. Calculate the moment of each force. In this step, the magnitudes of the individual forces and their distances to the chosen axis or point are multiplied to calculate their respective moments. Here, the moment of a force is a vector quantity, and its direction is perpendicular to the plane of the force and the chosen axis or point.
5. Sum the moments. Once the moments of all the forces have been calculated, they must be algebraically summed to obtain the net moment acting on the system.
6. Determine the effect of the net moment. If the net moment is zero, there is no rotational motion. If the net moment is negative, the object will rotate clockwise, and if the net moment is positive, the object will rotate counterclockwise.
7. Solve the problem. The final step of problem-solving is to use the calculated net moment to solve the given problem. For instance, if the angular acceleration of an object needs to be calculated, the net moment acting on the object is divided by the moment of inertia of the object.