Final answer:
To add moments, add the magnitude of their relevant directional components. Use the Pythagorean theorem for the resultant magnitude and trigonometry for direction.
Step-by-step explanation:
In order to add moments together, you simply add the magnitudes of their components along the same axis. For instance, you would add the x-components of all moments together to find the total moment in the x-direction, and similarly add all y-components for the y-direction. Once you have these components, you can then use the Pythagorean theorem to calculate the magnitude of the resultant vector, and trigonometric functions like the arctangent to find its direction relative to a chosen axis.
It's important to ensure you consider the correct signs for each component based on your choice of the positive direction. Positive direction must be consistent throughout the calculation to achieve the correct resultant moment. For scalar multiplication, it's also key to remember that dividing is akin to multiplying by a scalar that is the reciprocal of the divisor.