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.
Fig. 1: Example 1 (I apologise on behalf of my Nokia 3 for the poor image quality)
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.
Is failing the National Talent Search Examination (NTSE) the end of the world? No.
When I failed to clear the final interview, I was so depressed that I came down with severe high temperature fever, and had to skip school for a week or so. I’m also pretty sure it started a chain of events that indirectly led to poor performance in my 12th standard board exams, and eventually my university entrance examinations. Of course, I am to blame for my own failures and under-performances. I have made my fair share of mistakes growing up, and I continue to learn from them on a daily basis.
I have been in that situation on multiple occasions since, between the years of then and now, which is about a decade. Believe me, it is not the end of the world. It is not even the beginning of what you are going to face in the coming years of your life.
Stop looking to “balance“ school and NTSE. It is a term that people use to add unnecessary stress and pressure on to themselves. In my personal opinion, they both complement each other. Looking back, NTSE preparation taught me shortcuts and memory hacks that I subconsciously used in my 10th standard preparation as well.
Don’t balance anything. Give each aspect of your life the attention it rightly deserves- academics, co-curricular, extra-curricular, sports and hobbies.
In Mechanics, strain is defined as the ratio of change in dimension to original dimension of a body when it is deformed. It is a dimensionless quantity as it is a ratio between two quantities of same dimension. When a body is under load, it will extend in the direction of the stress (longitudinal strain) and contract in the transverse or lateral direction (lateral strain), in case of longitudinal tensile stress.
To learn with example, take a broken rubber band.
Holding one end in each hand, stretch one of the ends. The length increases. The ratio of change in length to original length is called the longitudinal strain. You will also notice that the rubber band gets thinner as you pull it further apart. The diameter/breadth reduces. The ratio of change in diameter/breadth to original diameter/breadth is called the lateral strain.
Furthermore, the ratio of lateral strain to longitudinal strain is called the Poisson’s ratio.
Poisson’s ratio is independent of cross section. As far as material is concerned, Poisson’s ratio is determined by two independent factors, i.e., the solid rock and dry or wet cracks. The former is influenced by the constituent mineral composition. Poisson’s ratio of the solid rock may be roughly estimated from clay contents for clastic rocks.
Cracks lower the Poisson’s ratio in dry rocks and increase the Poisson’s ratio in wet rocks. The magnitude of change depends on the volume concentration and aspect ratio of cracks. The higher the pore volume concentration and the lower the aspect ratio, the larger is the amount of change in Poisson’s ratio.