I talked about memorization (Read: Memorization Made Easy & Fun) in an earlier post, two years ago. Today, I was helping a friend out, who is in her second year of engineering, and I was reminded of my Air Violin Method of balancing moments.
One can take moments around any axis at any location as long as you are consistent with the directions i.e. clockwise moments balance the counter clockwise.
The Air Violin Method
Use your left arm as the axis (x, y or z as per case) and use your right hand to imagine each force going around it. Count those that do, neglect those that go through the arm.
The forces that go over the arm (counter clockwise) are negative. The forces that go under the arm (clockwise) are positive. This is just a notation for consistency. It is a matter of perspective. One can also use the reverse.
Let us use another example:
To take the moments about the x-axis, I imagined the x-axis as my left arm (shoulder to fingertips, left to right). My arm is aligned with Ax. Anything that went clockwise around my arm, I take it as positive. Counter clockwise is negative. For example, Bz goes counter clockwise, hence is negative. Cy goes through my arm, hence it does not count.
Anything touching my arm does not count. Moments do not like touching. Only forces that keep a distance from my arm get to have their moment. See what I did there?
I call it the Air Violin Method because that is how you will appear to a person from a distance when you are solving it. Eventually, with enough practice, you will start imagining the air violin in your head and will no longer have to wave your hands about.
For now, make music like nobody’s watching.